The marker for the players location on a locator map is offset a few pixels depending on the hand holding the map.
Left hand: player marker is offset to the west
Right hand: player marker is offset to the east

Attached screenshots show this. I placed a cross of cobblestone and I'm standing directly in the middle and made screenshots looking in all directions. I would expect the player marker be displayed in the center point of the cross. Maps are level 2/4 but the offset is show on other scales too.

The fact that one is a simple map and the other one is a hidden treasure map makes no difference. When the maps are switched between the hands, the offset switches too.

The last screenshot has additionally placed the map in a frame directly on the stone I'm standing on. You see the player markers have an offset from the green item frame marker.