My watch and phone work really well together, if I'm wearing my watch then notifications pop up there first and don't show on my phone. When I take my watch off or when I'm using my phone the notifications appear on my phone.
However on my girlfriends watch the notifications pop up first on her phone, then on her watch a couple of second later, no matter the 'state' of either device. I can't find any setting mismatches. Is there a setting somewhere which causes the behaviour I'm getting?