Do you mean that they charge you an additional $5 (so in a 12 month period, exceeding the 300 search limit would result in 13 payments instead of 12), or does the next month’s subscription payment get moved up to the day that you ran out searches, with the number of payments remaining the same?

They update your monthly subscription's bill date to reflect the reup on 300 searches for the date of the 301st search.