Martin_NZ:

 

If your phone and the mini detect the trigger phrase the mini seems to take priority and the command is only executed on one.

 

Yes, this is what happens for me. If I issue a command then my phone will run the Google Assistant and I can see it analyze what I've said but then it closes and the Home mini answers.

My problem is that when I'm away from home then my phone ignores me when I say "hey Google", it only works when I'm at home. I've got no idea why, but I've got a hazy memory of answering a question as part of the Home setup that was asking me to decide something about when Google Assistant should work on my phone. Maybe I somehow told it to only work at home and not when I'm off my home wifi, but I can't for the life of me find any settings like that in the Google Assistant options...