Expect little Arab or Berber settlement outside of any citadels founded to keep an eye out on the locals in case they try again. Maybe the Norse to make some attempt to conquer it.
I was going to say "if they do, they'll Christianize the way the ancestors of the Normans did!" and we just change dynastic names for the same outcome....
...but actually, would there be any compelling reason for pagan Norse to rush to Christianize, in this location?
The major one would be to facilitate ruling over their conquered (and hard to subdue, as
@King_Arthur above points out) populace. I don't suppose any strong Christian power existed at all close by that wasn't too much on the ropes for their own reasons to come in and fight the Nordic rulers at the invitation of the resistant commoners, so basically If the Norse are stubborn about adopting the regional version of Christianity, it is a formula for general unrest and troubled times. Which doesn't make it a lot easier for the Andalusian powers to come in--somewhat so, conceivably a number of Christian regional people might find it easier to make their peace with a Muslim overlord than endure Viking rulers. But that ought to motivate opportunistic Nordics to ally with their subjects.
Their alternative would be to accept Muslim overlordship, if the neighboring Muslim powers could offer them something or other useful toward dominating their populace; the benefit to the Moorish principalities involved seems obvious enough, if they can't foresee an Asturian Muslim analog to Normans horning in on their bailiwicks.
Which is a fun ATL--Islamicized Nordic Asturias sweeps down on the quarreling Andalusian powers and knocks them together into one strong centralized Muslim domain unifying the entire Iberian peninsula south of the Pyrenees!
But--it seems totally improbable, the only thing even more improbable is the Nordics refusing either Abrahamic religion and staying Aesiric for any long term. The best way for them to legitimize their rule and achieve command and integration into the conquered locals would be to Christianize pronto, and indeed individual Jarls who chose to this on their own hook would gain a competitive advantage over other lords who were slower to do so. Whereas I can't really think of any aid the regional Muslim powers could offer that would enable the Nordics to seal their control--if they could do this, they could conquer Asturias themselves I suppose.
So yeah, a wave of Vikings settling in Asturias comparable in magnitude to the founders of Normandy might jumpstart the Reconquista somewhat, if they replicate Robert the Devil's ruthless methods. That seems likely enough on general principles--but the question now is, are Asturias and Normandy at all comparable in terms of opportunity? In fact OTL the Norsemen landing on the Neustrian coast found the ruins of Rouen (whatever its Roman predecessor name was) and while the power structure Robert built some generations later was largely ad hoc and new, the ability of the ragtag gangs of opportunists to make something of their conquests and enable "Hrolf the Ganger" to defy Charles the Simple with the contempt he showed his nominal new overlord had a lot to do with being able to build on the infrastructure. The Neustrian coast had seen better days by far, but it was not at all the case the Norsemen were moving into empty wilderness.
Asturia too was not empty wilderness of course, but again as
@King_Arthur also noted, its people took advantage of their terrain and so forth to discourage and limit the ability of any outsiders whatsoever to subordinate them or integrate them into their grander schemes.
It seems far more analogous to Brittany than Normandy--whether the land could produce comparable numbers of people or not, it is far more difficult given the terrain to exploit them and skim off a surplus to sustain a powerful force of noble fighters. It might indeed be land well suited to produce defenders but not attackers in remarkable numbers, nor one to favor a powerful centralizing overlord.
Thus, if we envision the incoming Nordics as linking up to the native people overnight and even if we imagine a would-be Robert carving out a feudal hierarchy of it, the material he would be working with would be far less suitable to conquering adventures than the relatively rich and developed lands of Normandy. Nor would there be rich domains such as England or Anjou near at hand to seize control of by conquest or dynastic marriage--Muslim Iberia indeed would be worth taking but hardly easy to take, and the zones of greatest value would be distant.
It seems then that there would be little particular attraction to wandering sea raiders to put in and set up shop on these shores. Perhaps the port towns themselves would be worthy of seizing, but projecting power into the hinterland would be an uphill struggle, almost literally, and without deep ties inland, the ports are of dubious value. Perhaps some Nordics did settle there, and the modern population has absorbed their small contribution without their having opportunity to go on to more grandiose things. Perhaps they steered away looking for richer plunder.