Let me explain more clearly. On, for instance, R500,000 debt 1% interest = R13.70 per day.
It is irrelevant when the debit order goes off - if it is to late to include the new rate then it will reflect in the next debit order (typically the "debit order pipeline" is loaded a couple of days before it is executed).
Interest is calculated daily. Should the banks drop the rate on 30/4 it means that you save R13.70 on the day (and for the month of April). If it is too late to change the debit order your next one will be R13,70 less (plus off course R13.70 x 31 for every day of May at the new rate).
If they change on 1/5 then it is a moot point. Referring to the OP - whether they change the rate on 30/4 or 1/5 is not going to make a big difference - you still accrued daily interest on the old rate for most (if not all) of April.
Yes, the saving on May's debit order will not be minuscule. But it is for April.