I would be very surprised if Monzo aren’t crediting the account the “instant” they receive the notification from the sending bank. The reason you may have heard the “2-3am” figure is that they may be when some older/legacy banks actually run their batch processes and push the payments out (which the receiving bank can then handle instantly in the case of Monzo).
If you are actually seeing the 2-3am delay on Monzo and you know you weren’t on your other accounts, could you let Monzo know which sort code (no need for the account number) the payment is being sent FROM so they could track it down.
It might also be the fact that some banks send a notification before they send the money and your other bank accounts are appearing to act on that instruction instead of waiting until the money actually hits (i.e. similar to how Monzo handles card payments - they show the ‘Pending’ debit when they receive notification money is likely to be taken, but it isn’t actually taken until “Authorised” a few days/hours later).