We use our fresh water at rest stops while travelling and will sometimes get maybe 5-10 seconds of water flow if we've forgotten to turn the pump on before opening the faucet. Never 30 seconds.
Maybe when you shut off the faucet, the pump doesn't shut off right away. I would assume the pump has a pressure sensor that turns it on and off. If it's running for 5 or 10 seconds after you close the faucet, it's building up pressure between the pump and faucet(s), which could act like an accumulator. You should be able to test this as a theory by listening to the pump as you shut the faucet.
A less likely theory would be pressure buildup in the fresh tank. That would assume that the pressure causes water flow through the pump without the pump actually being energized electrically. You might be able to test this theory by opening the fresh tank drain valve. If water comes out forcefully, like from the nozzle you put on a hose, it's probably under pressure. My experience draining the tank is that it flows freely, but not forcefully. You might also be able to observe and feel the pump while faucets are opened and closed to try to determine if water if flowing through the pump when it's not energized. I would expect that any excess pressure would bleed off after a few uses and the cycle time would eventually get back to normal (as if no accumulator).
A lot of people have trouble filling the fresh tank. If you're forcing water into your fresh tank to fill it (rather than allowing gravity flow of the water), and your tank vent line is blocked, you may be pressurizing the tank without realizing it.
In any case, excess pressure in the system sounds like a good way to end up with a water leak or ruptured tank. You should keep looking for the cause.