I am experimenting Push/Ableton in my live mixes.
I managed to configure DJM and Ableton so that Ableton matches the BPM of my DJM (DJM sends MIDI clock to Ableton, which is done in Ableton config).
Although I have the same BPM they are out of sync

I was naively thinking that Ableton would be able to match the bits based on the quantisation set in Ableton. Is it not the case?
When I hit the MIDI start/stop on my DJM Ableton starts playing at the correct BPM but quantisation is not taken into account.
Questions:
A) Is there any way to tell Ableton to start playing not only with the DJM BPM (this is working) but also to use quantisation to make sure the bits are not out of sync? I have the feeling that the "MIDI start / stop" button of the DJM is not to be used to trigger Ableton anytime during a live set but rather at the beginning of the show, ONCE, then match bits with nudge in Ableton GUI then, once it is in sync don't touch the "MIDI start / stop" button again. which is a shame as I was under the impression that MIDI and Ableton would take quantisation into account...
B) Nudge not working if I enable external MIDI clock: It seems anytime I tell Ableton to use external MIDI clock (in my case my DJM's) the Nudge buttons in Ableton GUI stop working. I disable external MIDI clock and it works again. Any thoughts?
Thank you all in advance.