Upon further testing, it seems there's another bug:
Casting a jump skill with "CharacterUseSkillAtPosition" seems to ignore all animations/effects, and just teleports the character to the position. I've tried it with Phoenix Dive also, and it gets the same results.
Likewise, casting my target spell with the jump animation through a story script (CharacterUseSkillAtPosition and CharacterUseSkill) has the same problem.
Edit: Whoops, seems that latest "bug" was actually just a result of not delaying the next skill cast long enough - I added some more time to my timer and it plays the animations correctly now. Still experiencing the bug in the original post of course, but I may be able to work around it through a script.