(. . .) still not sure why we didn't have permission to move them when he made duplicates on the new map?
That is odd. At risk of saying what you already know, the duplicated tokens transferred to a new map keep the player permissions set by the GM, regardless the map.
Just in case, let me say that these permissions are to be found in a menu field -in the token edit window- called "Controlled By". The GM puts there the names of the players allowed to control the token, an such permissions are indeed transferred over maps.
I don't know; likely the GM forgot to put the permissions right (your player names), but I don't try to blame him; then, if that wasn't the case, it could be an odd glitch. For reporting it as a true problem or bug, you'll need to be able to duplicate it. So I'd test it again, being sure of setting the permissions correctly.
If after setting the "Controlled By" fields (permissions) the problem appears again, please post about it again with your computer, OS and web browser specs.
For what is worth I just tested once again the "Controlled By" field and then entered to the game as a player with permission, and it's working OK with tokens copied and pasted from another map, without any need of putting the permissions again.
Regards