Condensed version of how it works:

The EVAP system is supposed to prevent fuel vapors from escaping into the atmosphere. The fuel tank is vented through a carbon canister via the canister vent solenoid which is controlled by the PCM's programming. During normal driving, the vent is open allowing air into (or out of) the fuel tank through the canister.

Since the vapor system is supposed to be closed for the fuel vapors, it must be tested periodically. The PCM does this by closing the vent solenoid, opening the purge valve to apply manifold vacuum to the system, them measuring the air pressure (vaccuum) inside the tank using the fuel tank pressure sensor located in the top of the fuel tank. A properly sealed system will bleed up vacuum within a certain amount of time. The system the shuts the purge solenoid and measures bleed-down time to verify system is sealed. Leaks can be identified by the rate of bleed down and classified as large or small.

After fueling, as detected by the fuel level sender in the tank, the system runs a "mini-check to verify it can draw a vacuum on the tank. If the system cannot draw a vacuum, it concludes that the fuel cap is probably not sealed and lights the fuel cap warning light.

Now, to your specific instance:

1) Next time, don't futz with the battery. Just pull the PCM KAM fuse if you want to reset the PCM's memory. That way, you don't have to reprogram the radio!

2) Resetting the computer as you did makes it so the fuel cap "mini-check" wasn't run since it only runs after you fill up the tank. You just turned off the light, but the underlying problem may (and very likely still does) exist. You'll find out the next time you refuel. Don't be too surprised if you happen to get a MIL with an evaporative emissions leak DTC in the meantime. If it does, you're going to need advice or assistance from someone who knows what they're doing or talking about...