Ken Adams has posted a useful annotated essay about the distinction between "promptly" and "immediately." I agree with his conclusion:

Because immediately seems to promise more than it can deliver, you should omit it from your contracts. Use promptly instead. If you want a standard more demanding than promptly, specify a limit in days. Or combine the two standards—promptly, but in no event later than X days after ….

Pactix contract clauses contain no instances of "immediately" that I can think of; they all use "promptly," as Ken suggests.