Objects both move onto the same spot in the same frame

I'm currently making a 2D game with a view from the side and it has grid based movement. All objects have a move point that moves 1 unit away at a time and stops moving until they catch up to it. I'm using Physics2D.OverlapCircle to test if there is another object in the way at the time when the move point is trying to move.

The issue arises whenever 2 objects check at the same time to move onto the same grid spot. Both of them see nothing is there and move their move point onto it and then they overlap at that spot.
I'm fairly new to Unity and I'm not really sure where to start with trying to fix this. Help is appreciated.