Hm ... things can be so easy!
Thanks.
//EDIT:
OK, doesn't seem to be so easy at all.
I activated the debug mode, but I still can't change a template's product assignment, and I still can't create a template belonging to a different product than vBulletin.
I can select my Plugin's name from a dropdown box, but the product will change back to vBulletin after saving.
I gave my Product a name beginning with "vB". This should not be an issue, since you just are not allowed to let the Product ID begin with "vB2, but not the title. Also, I checked it with another Product named "test", and the Style manager won't "remember" the product assignment, too.
Does anybody know the reason for this strange behaviour?