I always thought the time delay was the time it takes the B/U pump to spin up enough pressure to pressurize the system via the shuttle valve. (Not for the electrical system to actually swap anything over.) My understanding of the system (in navy birds at least) is that the transfer module contains a spring loaded valve so that when Pri pressure drops below the limit, the shuttle is automatically moved by the spring and lack of pressure to allow the B/U system to power it.
One of the reasons we kept going back and forth in NATOPS procedures on when to move the B/U Pump to Auto vice On or Off was that some genius suddenly thought that we might be wearing out the shuttle valves on startup during that transition phase where the main pumps were still building up pressure and the B/U pump was running, thus giving the potential for the valve to flutter or some such.
To clarify, the delay is actually in the depressurization valve. The electrical relays and #2 logic module determine when the depressurization valve should stay open for 3-5 seconds, allowing the backup pump to come online and to protect the current limiters when neither main generator is online.
Regarding the transfer module, what you said is mostly true. However, the transfer to the #2 T/R servo happens a little differently, since it operates independently of the secondary shuttoff of the #1 transfer module (which is the #1 T/R shutoff). If you remember, the #2 T/R servo is on the deck of the hydraulics bay aft of the primary servos and to the right of centerline. It is totally separate from the utility module and the #1 transfer module.