Quoting Patrick J. Geary, one of the leading specialists on Merovingian period.
Theuderic (Thierry) I benefits from the crisis that the reconquest of Italy plundges not only the peninsula itself, but also in more northern Alpine regions, intending to annex most of it. He begins by submitting what remains of Thuringians, these most ancient clients of Ostrogoths. In the North he imposed on Saxons a quite relaxed control.
His son Theudeubert goes further. The abandon of Provence by Ostrogoths isolate Alamans [...]. Theudeubert submit and annex them, as are the alpine regions occupied by Raetho-Romans, particularily in Coire. Further East, he sumbit to his rule an amalgam of various peoples : Thuringians, Lombards, Heruli, Veti, Alemani, and others that combined with the remaining Roman population of Norica to form the people of Bavarii.
This map is particularily crude (I'm almost tempted to ditch my work on 117 and 1520 AD to do something better there), but gives a good general idea of the situation in the VIth.
Clothar was probably less interested on the region overall, apart from possible ressource pool, especially for his goal of unifying the frankish kingship at his benefit : let's remember Franks made an extensive use of mercenaries/allies/federated peoples, and we know that they used Saxons from Germania in their battles. For instance, Theudeubert used Saxons at his side during the Battle of Zulpich and giving their association with Thuringians as well the the courts of Theudeubert, it was certainly not Armorican Saxons there.
In fact, Merovingians seems to have been content to have a series of associated peoples, more or less controlled, in Germania as part of a clientele network. Saxons on this regard, were their least concern compared to peoples as Bavarii and Alemani that could serve against Italians or Wendes (or at least, could be allied to these, and had to be held in check). But, in the context of the VIth and VIIth centuries, when contemporary chroniclers says the Saxons revolted against Clothar (or other kings), it's essentially the case : largely autonomous peoples banding togther against Merovingian hegemony with various fortunes.
Eventually, what Franks seems to have tried to establish in Germania, was to re-establish at their scale, with conceptions and conditions that obviously changed (both in Romania and in Germania), the old clientele network of the Late Empire, doing so on the ruins of Theodoric's own network. Talking of revolts of Saxons against Franks is no more strange than revolt of Alamans against Romans (all proportions kept, of course).
Theudeubert in particular seems to have tried to impose the fiscal and institutional pattern of Gaul in Germania. I'm not saying that Franks could have pulled a "Gallicisation" of Germania (or even attempted it entierly : as said, the clientele/federal model suited them enough in the VIth and VIIth centuries), but it's hard to not consider the possible increased pressure when ooking at fiscals troubles in Gaul.
The tribute was possibly broken, in the same time as the royal
faida led to a partial political withdrawal from Germania (altough some kings did launched campaigns against Saxons), and if abandoned at all, was re-established by Clothar II and Dabgobert I : always at sword-point, of course, but there's rarely other means to exert a tribute.
Quoting another specialist of Merovingian Francia, Ian Wood.
Less accessible to the Merovingians, Saxony was nevertheless subject to their influence. Gregory of Tours implies that the Saxons became a subject people in the time of Theuderic I, and he clearly regarded them in the mid-550s when they defeated Chlothar I. Although Gregory has no more to say about Saxony, it appears that before Chlothar died he re-established Frankish overlordship and forced the Saxons to pay an annual tribute of five hundred cows. According to Fredegar this arrangement continued until the time of Dagobert I, when the Saxons offered to provide military protection of the eastern frontier against the Wends instead. In fact it is debatable whether tribute was paid annually from the time of Chlothar I trough to that of Dagovert I, since ther is a reference in the Liber Historiae Francorum to Chilperic and Sigibert I campaigning against the Saxons, which may find some support in the opems of Venantius Fortunatus.
I'll go quickly over the relations between Franks and Saxons during the VIIth, if you will, prior to the Merovingian decline.
Royal
faida (roughly speaking, the endless infighting between branches of Merovingians during the VIth century), without doubt, weakened the Frankish dominance over Germanic principalties altough, as we saw on the Battle of Zulpich, relations were maintained even with Saxons. For what matter Clothar's campaigns, we have to point that Saxons (led by Berthoald) were allied to Austrasians in a similar fashion they were to Theudeubert.
We have in 620's, in the courts of Austrasia recently re-established at the benefit of Dagobert, a Saxon duke (Aighina, Aega, there's a lot of various transcription), whom authority is found on the right side of the Rhine (basically in charge of "submitted" Saxons between Rhine and Weser) and essentially military-based. I'll spare you the details of court politics, but it's essentially a fight between Aighina and Austrasian families which degenerate in faida; eventually Aighina is removed from Austrasia, with Berthoald in charge of a group of Saxons.
It's not really clear if Berthoald was trusted with Aighina's direction, if he simply filled the void, if he was a competitor or not. What's interesting is that a Saxon duke (you probably had more than one or two of these) is part of Frankish court politics, integrated enough to provoke a faida, and is apprently dissimised and in inner exile in Francia afterwards (possibly recycled into military commander in Vasconia in the 630's, fighting Vascons with Saxon troops, altough it's generally considered to be an homonym)
The Saxon "revolt" (we saw that the term isn't illegitim, but I agree that we're in an in-between situation there) of 627 does happen at a crucial moment, when Austrasia lacks a military command (due to the void let by Aighina from one hand, and the one let by the majordomo he murdered). Again, we have a duke at the very least dependent on the political situation in Francia for what matters his own.
That Fredegar points that Berthoald was (on his own words)
servus, in the sense of subordinated, of Clothar is quite interesting. I won't go into the details, but Helmut Reimitz makes, IMO, a good point about how it's on line with Berthoald's general behaviour (basically saying that it would be not that prestigious for Clothar to kill a servent, but a servent to kill a king,on the other hand...). At this point, the claim of Franks on having at least some form of hegemony over Saxons was acknowledged, if diversely accepted : the victory of Clothat against Saxons at Aachen, and Dagobert own's victorious campaign were made along these lines.
Regardless if Berthoald considered himself or not as subservent to Franks (and it appears he at least acknowledged the general idea), Frankish victories certainly put the concept in practice in some forms : for exemple, the tribute in heads of cattle is confirmed (altough possibly lowered to 400 heads according the LHF), and Clothar put little aftertought killing part of the Saxon aristocracy in late 620's : if "aristrocracide" is the marker of dominance you find decisive (and I agree it could be so depending on the situation) then it's worth noting that Franks underwent this as early as Clothar II's reign (altough it was made as an aftermath of the victirious campaign of Clothar, I also agree that its scope might have been much lesser than Charlemagne's)
Eventually, Saxons are largely unheard of for a time. Vascons (which continuously raid and revolt in southern-western Gaul) and even more Slavs (they didn't magically prevented to pressure Francia as much as they did in Balkans) are clearly a more important worry for Dagobert, but as well for Saxons that negociate an abandonment of the cattle tribute, in exchange of their military subservience in the mid-630's.
Not to say that Saxons were part to the same extent Thuringians, Alamans or even Bavarians were of the Merovingian ensemble: but they do seem to have been
going this way IOTL, tough, until the crisis of the VIIth century, the way Merovingian Germania was : a network of autonomous principalties under Merovingian hegemony; and not what was enacted rushingly by Carolingians that had to take back more sophisticated polities under their control, whom people and aristocracy certainly didn't want to go back (or to forcifully enter completly) Francia.
On several regards, we could make a distinction (largely historiographical : I doubt it would have been clear between Thuringians and Saxons in the 630's) between peoples/territories within the regnum, such as Bavaria, Thuringia, Vasconia; and their equivalent outside (while possibly acknowledging a certain Frankish supremacy or hegemony at times) such as Brittany, Saxony, Kent.