It's called 'APU on demand' & is where you would only start the APU if required by the loss of a generator. Periodically the APU is required to be started at altitude after cold soaking, in order to validate the requirement that it will start when required. This is usually indicated to the crew by a tech log entry from the engineers.
The other two possible APU procedures for ETOPS on the B737 are leaving it running after engine start until the ETOPS exit point, or shutting it down after engine start & starting it again prior to the ETOPS entry point. Both of these require the APU to be running during the ETOPS portion of the flight so that the APU generator is immediately available if one of the other generators fail.
Regarding the cross-feed valve, our mob require an operational check during the pre-flight duties of the F/O, as well as during the last hour of cruise, in order to check its operation when cold soaked. Aircraft with dual cross-feed valves don't require these checks.