But this is the sort of thing that Hitler did. He was under no obligation to interfere in the disputes over Slovakia, Ruthenia, Transylvania, and the Cadrilateral, yet he did. He'll very likely do the same for Dalmatia. He won't let it be a matter between Italy and Yugoslavia because that risks leading to an attack by the former against the latter, and that's exactly the sort of situation in which the Fuhrer invited his allies to Vienna to award territory to the most likely aggressor and thus keep the peace within his camp.
With fascist Croatia in OTL Mussolini was holding all the cards - Hitler hadn't even wanted a Croatian puppet initially, wishing to them over to Hungary. Mussolini was able to secure some nice possessions east of the Adriatic and sabotage Croatian designs on Montenegro and the Sandzak. With Yugoslavia in TTL he will have a fight - the recent fiasco in Greece showed that Italy was in no position to make offers that couldn't be refused. And another fight in the Balkans to delay Barbarossa is exactly what Hitler doesn't want right now.
So the outcome will be quite simple. After the subjugation of Greece, Mussolini will make demands on Dalmatia, on the pretext of protecting the rights of Italians in the region. (A very unpopular treaty in the late '20s forced Yugoslavia to allow Italian immigration, but even so Mussolini will have to inflate their numbers.) Germany will be facing the prospect of a war it doesn't need. There will be a meeting between King Paul and some high-ranking Nazi, maybe Hitler himself, in which it will be made clear to him that the 3rd Reich is very displeased at his country having the impudence of being the target of Italian imperial designs. He will be given the choice between a German arbitration which, given Paul's lack of demands towards Italy, will maintain the status quo at best or give Mussolini everything he wants at worst, and Hitler joining with Mussolini in an attack on Yugoslavia to ensure a quick victory, a threat made in the hope that it will not have to be carried out.