Your payment is all electronic and computerized. Once you pay, it is automatically linked to your account and gives it the all clear to process usually within 1 business day. 2 at most.
Your documents however need to be reviewed by humans to make sure they comply with the requirements and usually take longer. I would give them at least 10 business days before panicking. Once that times has passed, call them and verify they got the documents.
Obligatory: You should have known better than to wait till the deadline to sort your documents out.
That being said, whenever I have had to deal with official government departments, it takes a week or two for their systems/processes to catch up. As long as your document was submitted before the deadline, you have nothing to worry about. Submission date is all that matters regardless of them checking your file this week or 6 weeks from now. As long as you faxed/emailed your stuff before the cutoff, you have nothing to worry about.
Good luck!