I managed to get the conflict in monitoring by setting ALL asr rules to block and in another to audit. Conflict appeated immidiatelly. Now the question is, why some specific rule does not cause it, but some other does. The single rule I played before was WMI & PSexec block, that did not cause a conflict.
I also monitored local event logs with asr rules xml, and unfortunatelly that does not display the conflict coming from Intune policies.