The marker does drift indeed, but how much it drifts depends on which version you’re using
I made a CodePen snippet to debug the drifting when I made the CSS snippet version and now I added a date selector to it, so it’s even easier to test the drift effect: https://codepen.io/taneltm/pen/eYyeyBe
For the CSS snippet version, the marker will drift on top of the month separator gap, but the first day of each month should be correct.