IMO Fantasmic! is only roughly derivative of Fantasia. You should definitely have them watch The Sorcerer's Apprentice. That's cute and kid friendly, and that has the most that scans to Fantasmic! They'll also recognize the scene in Philharmagic as well. There are some scenes from the other parts of Fantasia but having seen the movie isn't essential to enjoying them as they're essentially beautiful images that go alone with music and can be enjoyed independent of their larger stories. If the kids really love Sorcerer's Apprentice, then you can go from there. To get kids into the musical package film genre, I think Fun and Fancy Free and Three Caballeros are more kid friendly than a lot of Fantasia.
Chernabog, IMO the most important/identifiable villain in Fantasia doesn't even make a big appearance in F! Edited: i just rewatched it to check this because I figured there should be, and there is about a minute of on-screen "Night on Bald Mtn" footage, but I don't think it's necessary to see it to appreciate it. He basically looks evil, so the kids will get the picture,
I think they'd recognize a lot more if you started with the other classic Disney films. The Evil Queen Grimhilde from Snow White features prominently so they should definitely watch that (I'm also a huge Snow White fan and it's an important part of film and Disney history) as does Maleficent and her dragon form. If you had to choose just a few things, I would say The Sorcerer's Apprentice from Fantasia, Snow White, and Sleeping Beauty would be the best place to start.
ETA: Snow White and Sleeping Beauty aren't really that girly. Tell them about the amazing battle at the end of SB.
if they absolutely refuse the Princess movies, then try for Peter Pan and Aladdin as Captain Hook and Jafar make an appearance.