Whilst my memory is slightly iffy, when I was working in a professional lab doing Dip 'N' Dunk C41 and E6 processors, among other processes. Whenever we had E6 go through the C41 bath, we immediately ran a control strip through the C41 after the E6 film was out of the first bath.
After checking the control strip, some manual adjustments would be made, then we would invariably run one or two unimportant 8x10" sheets of C41 through the C41 bath, then another control strip. After this we would invariably do some manual adjustments to the first bath then run another control strip through.
Now we were running a very tight ship and the C41 process would quickly settle down, but it did upset the developing bath somewhat, and as a good proportion of our C41 process was taken up with processing Kodak Color Print film, which gives one a transparency, our process had to be spot on.