I couldn't see very well either in his images, but what I *think* I saw was the existing tracks seemed off compared to the grid. The EZDrum seemed on.
So if played alone the existing tracks would sound fine, but with EZDrum (or others aligned to the tempo map) things get off.
Can you easily create a 'click' or metronome in Bandlabs that aligns with the tempo map?
If EZDrums aligns to it, and the imported BiaB tracks do not, then the click track (tempo map) would be suspect.
Or maybe some loop metadata.

Just trying to help find a quick way to figure out which is causing the problem.

I do not work here, but the benefits are still awesome
Make your sound your own!