You are not over-thinking. We are OCD detailers after all. I went through the exact thoughts myself but I couldn't really find a definite answer. Maybe I'll get the answer here.
I also scrub both sides of my mitts against the rinse bucket but I don't do it in the soap bucket.
I also wring out my wash mitt after the rinse bucket and before dunking it into the soapy bucket. I don't want to dilute the soap solution.
I also wonder like you, OP, if the scrubbing causes turbulence inside the bucket and causes the grit/dirt to go up and catch in the wash mitt.