Depends on which version the core is from I guess.
The one that comes along with ZMZ seems to work here fine (it wouldn't hurt testing though).
Back on topic: I played your levels (at least the normal ones, no secret exits found if there were any). It's overall a pretty fun hack. However, I'd like to call your attention to graphics: I know you're a ripper and use your own resources feels pretty good, but be careful with clashes. The cave graphics you used are pretty 3D-ish and can look bad if you compare it to the 2D-ish grassland. I really liked your graphics though, especially your backgrounds! I should take a look at your rips thread sometime.
Regarding the training level: I don't think blocking all holes in it is a good idea if done this way. You could've designed the level so it wouldn't have any holes, I guess it would make more sense. Anyway, I don't think blocking them is that all necessary, because there are other ways to die (one of them being standing above the exploding platform when it timeouts - you mentioned in the message box, but I honestly didn't know the explosion would kill me :/).
Also I guess you're already aware of that, but that goal sphere will make Mario walk to the left if it's taken from the left; make sure you'll design every goal sphere around that if you're going to keep it this way. Avoid leaving a chance of Mario dying when taking a goal (but blocking his way with a wall or block looks rather weird in my oppinion, so I'd give priority to letting him walk without dying by both sides).
Other than those nipticks, it was a pretty enjoyable demo; hope to see more from you, about both hacks and graphics! :D