chas:

Does the change in idle occur immediately with the replacement of the tank cap?, or is there a delay of a minute or two?

There is no functional reason for the tank to be closed for the engine to operate; the closure is for the purpose of controlling evaporative emissions. If the change in idle characteristics occurs immediately, there may be an air leak or stuck purge valve in the evaporative control system.

Typically, after operating for a period of time, the tank will exhibit a slight overpressure, rather than an underpressure.