There is no RefreshCounter macro in the workbook shown, so it's hard for anything to work.
Changing the fill color of a cell doesn't trigger typical Excel events, which would be useful for forcing a recalculation of formulas. Admittedly, there are methods that can replace Excel events, but each of them has some drawbacks.
If you accept manually forcing the recalculation of formulas, then one of the following three macros associated with the button should help.
The first two macros refer to the source ranges of the GetColorCount formulas. "Changing" the values (even if they are the same values) in the cells referenced by the function causes the function to recalculate.
The third macro forces recalculation of all formulas (not just GetColorCount) in the active sheet.
The choice of method is up to you.
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