Player and AI character play animation with each other but sometimes they "miss"

My player does animation montage when its special collision capsule is overlapped by AI character, which, in turn, does animation via its “state” in animBP. I make them stop movement and turn toward each other, and it works for most cases, but sometimes they sort of “miss” each other - and that looks awful. Somehow their rotation is shifting and location is shifted so they do animation in a distance. This happens when they meet at a certain angle, especially if AI character is in the jump move or they run towards each other.
I sense that this has to do with “physics,” of which I know little. How to disable all physics and let them do their animation at the moment of overlapping capsules. Any advice or links? Please help!