I struggled with this today with two specific devices, a raspberry pi and a debian linux machine, I could ping other devices next to them on the two remote networks, but not each other.
The solution that finally got them to work was as follows:
On both machines run the following to find your ID
sudo zerotier-cli info
200 info **999xxxxx99** 1.6.2 ONLINE
you need to copy that ID
On each machine, stop the zerotier service
sudo systemctl stop zerotier-one
Once they are off, you can delete the peer info on both machines
sudo rm /var/lib/zerotier-one/peers.d/999xxxxx99.peer
After you do that on both machines, restart the zerotier service
sudo systemctl start zerotier-one
They should now be able to communicate within a minute or so.
I hope this saves someone as much time as it took me to write this up.