I think non-master processes trying to log something, but have no Logger instance because have no Task instance.

Hmm is your code calling Logger.current_logger() directly ?

Logs in master process include all training history or I need to concatenate logs from different nodes somehow?

So the main problem is that you need to pass the TASK ID that the master node creates to the second node, so it can report to the same Task.
I know that the enterprise version of ClearML supports SLURM and does exactly that (actually the launching itself is from the ClearML UI and slurm does the scheduling, and then everything is taken care of)
Can you think of a way to pass info from master to second node ? You can always of course limit reporting in your code in case you are not the master