I would fill the top 2 first as a pair then the overflow from those fills the bottom pair, then excess can be dealt with.
Of course one issue, if there is to be only one outlet is how to connect the top and bottom without a manual changeover. That can be done with a oneway valve so the top ones don’t drain into the bottom ones.
Edit: to deal with air being sucked in consider a second oneway valve above the outlet as shown, once the upper tanks no longer have water then the valve will close.
Once the top pair are full the fill to lower tanks takes the excess until the lower tanks are full then the overflow bottom left controls the final level.
The outlet is fed from the top tanks until empty, then the oneway valve allows water out to the outlet from the lower tanks. If you don't have the oneway valve the top tanks will just empty into the lower tanks.
This has the advantage that the lids are now just dustcovers and are easy to remove / replace for cleaning.