You have to be aware at all times when open. When you open, you need to be watching everything. Pilots may do this, taxiing without permission.
In order for a pilot to taxi they must receive clearance to do so from the ground controller, they can’t taxi without that permission.
If an aircraft begins to taxi without permission, whether that be after push back or not, they must be on guarded. It should only take you two or three seconds to realize that there is movement.
Once they’re on guarded send “Wait for clearance before taxiing”, then they’ll get the hint and request taxi. If they continue taxiing without requesting either report them or send a “Please follow instructions” command. If you send a “Please follow instructions” command and they continue, report.
They need that warning though and you need to always be aware.