I've yet to have a tame jump slots. Had a beetle be close to jumping slots, but I got all 4 taming sessions in on it.
What order are you guys training in? My lesser 1 slot got all 4 training sessions as well. On 1 slots and 2 slots I usually do Resists + dex/sta if not maxed on first round and the remaining points in HP. Second round I do HP to 600 and then remaining points in str or MR. 3rd round I finish off str around 700 (or max it) and finish off MR and HPR. Final round I'll use for skills and special moves.
Any points left over during rounds I'll put into int or mana. I think my Lesser Hiryu actually had enough points to max HPR, SR and MR and boost his HP to 700 with being 8x Legendary. I put Goo and Bushido on it.
On my blue beetle I noticed while applying points it went from 1 to 2 slots before finishing applying them all. But when I started training again, it remained a 2 slot pet, and went to three slot midway between applying the points again. Started training again and it stayed a 3 slot, then went to 4 when applying the points, and then was able to start the final training from 4 to 5 without issue. I'm wondering if there is an "order" of applying which will cause the pet to change?