If the same user is logged into multiple phones, does Connect send a push to all phones for the user? Or just one of them?
If the user is logged into the app as the same user AND the campaign has a frequency cap of 1 message per user, then it will only message the user once on whatever device they use first.
If the user is logged into multiple devices as multiple users OR the campaign has no frequency cap, they'll receive the message on all their devices.
See Using campaign frequency caps for more information.