Jim,
Thank you for detailed suggestions.
Yes, my midi files have tempo embedded, but it did not give me trouble before. I arranged several tunes in such manner.
I was able to find suitable real tracks or drums to replace or add to the composition.

Mike,
Thank you. Yes, I am paying attention to feel and "suggested" tempo range of RTs.
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Here is the thing. If I use same MIDI file and export a Real Track as WAV that are not in sync in BIAB and manually align these MIDI + WAV in DAW, everything playing as it should (in sync).

Ember(of PG) agreed to test it for me., I hope she will have a solution, as this workflow is crucial for me.