"Can you all please complete this form by putting a tick in the boxes"
'Tick' = Check
In other words the mark made when something is correct or selected.
So an American should not be alarmed if a Brit' says to them "I put a tick in the box". They are not infested with 'ticks' and generously presenting you with one!
Equally if you're a Brit' and an American suggests you need to "check them all", they are not asking you to look anything over closely.