It is independent of payday and, in order to maximize interest, the debits should happen as late as possible within the payment frame so they are not late.
For example, if you have to pay, say, utilities or mortgage or whatever, which relate to the calendar month, it makes most sense to pay them on the last calendar date.
It doesn't matter if your payday is the 1st, the 15th or the last - in all cases, the approach I describe maximizes your interest earnings.
But, depending on the amount we talk about and the interest rate, it might make more sense to not care about that and just take the approach to see it more important to have an overview of all "free" money you have.
Edit: In order to add a bit of personal experience:
My salary generally reaches my account on one of the last days of the months, in very rare cases on the 1st of the following month. I have a bunch of direct debits and automatic payments:
- on the 1st or 2nd, some insurances and some house costs
- utility bills around the 15th
- some minor fixed payments scattered over the month
- around the last (or 1st) a direct debit to a "house saving account" (Bausparvertrag, special kind of high interest saving account made for biolding purposes)
I don't like having too much money on the "checking account" (giro account in Germany, as we generally don't use checks any longer).
So I put the money which is after the 2nd or so on a savings account, from which I transfer some money back during the month as needed.
This way, I am independent of when the payments take place and it becomes an issue of convenience:
- For maximizing the interest, it would be better when all payments were due as late as possible,
- but for the sake of clarity, I would prefer when everything would be paid on the 2nd or 3rd.
Depending on when my salary comes in, the saving amount at the end of the month is paid from the "old" money (from last month) or, if it is already there, from the "new" money.