It sounds like it should be working, but there are several points where your description is vague. Ultimately, though, it will all boil down to what game you are attempting this in.
Are you playing in Sun/Moon/Ultra Sun/Ultra Moon? If that is the case, then I am extremely confused, because there should be no extra steps required. You've stated that you are breeding a female Alolan Vulpix, and it is taking place in Alola, so the eggs will hatch Alolan Vulpix. And that the male Sylveon has Moonblast as a move, so the Alolan Vulpix offspring should all know Moonblast. I can only assume, if this is the case, that you are mistaken about the Sylveon, and it does not know Moonblast, because it should be working otherwise.
Or are you doing this in Sword/Shield? Since you are breeding a region specific form, you need to be sure the parent is also of the specific regional form, and that it is holding an Everstone. If you do not do this, the offspring will all be the generic form. This is also critical in your case of Alolan Vulpix, because the standard Vulpix does not learn Moonblast in any way, while Alolan Vulpix does.
The only other possibility is that the offspring are learning too many moves from their parents, and so are somehow overwriting Moonblast. What moves do the offspring know? If their moveset is full, then it might be as simple as rearranging the order of the Sylveon's moves, so that Moonblast is the last thing the child learns from its parents. You could try moving Moonblast to the Sylveon's last move slot, to force this to occur. For extra safety, you could use the Move Deleter to remove the parent Alolan Vulpix's other moves. Just leave the minimum 1 move. If Moonblast is the only thing you need from the Sylveon, you could go ahead and remove everything else from it, as well, assuming you don't need to keep the Sylveon for anything else.