Sellers can open an "unpaid item case" in the Resolution Center as early as 4 days or up until 32 days after the listing ended if they do not receive payment. Buyers have up to 4 days after the case is opened to pay the seller.

The seller actually does not have the ability to open a case before 96 hours has elapsed. If a seller emails you threatening to open an unpaid item case before 96 hours has elapsed, you can technically report it as a policy violation.

"Pay promptly/ship promptly" works great and IMO is the norm on ebay. Dealing with dishonest people, however, is not easy or fast. How to deal with that requires a thread of it's own.