Should a leak repair take effect immediately?
Depends on what the real cause of the leak was and how it was fixed. The "leak" you saw may have been simply loose water that had already leaked (or was incidental to taking the plumbing apart to repair) and simply needed to drain.

Other products take some time to cure and be waterproof and pressure-resistant like Michael said. PVC pipe sealant and liquid thread sealants like LokTite take a while to dry, but again as Michael said they need to cure without any water pressure for best results. Other sealants are specifically designed to seal under pressure, but these are generally quick homeowner fixes (the equivalent of car radiator leak-stop) that a licensed plumber should not be using as a permanent fix to any problem. Teflon tape and other flexible solid seals, as well as solder, should be immediately waterproof.