I haven't seen anywhere that Apple has posted what algorithm they use for how often AirTags will send updates.
Apple employees that do participate in the forums here would never post information that hasn't been publicized (well, not unless they're an idiot) - doing so can cost them their jobs.
You also didn't state some pertinent info on the test you did. Your son has cellular data? Bluetooth is turned on? His phone isn't also using your Apple ID?
If your son's phone doesn't have cellular data turned on, then the location of the AirTag would only be sent when they had an alternate data path (Wifi) - if they didn't have that until they get home, then it would appear that the AirTag never left, in all likelihood.