How can I adjust a whole-house ventilation bathroom exhaust timer?
Look at the vent:  take the cover off and examine it for mechanisms, part numbers, etc. that you can see without taking it apart further.  Take photos and post it.

Likewise, take the trim plate off the switches and see if there's anything interesting or whether it's just a plain switch like any other.  

I installed a timer for the bathroom fan that's just a fancy switch, and it's quite obvious because it has time buttons and lights at the switch.  If your behavior is independent of the switch position it needs a power supply separate from the switch, and the switch may be wired funny even if it is a plain switch.

I'm guessing it's built into the fan unit.  IAC, it would have to accessible somewhere, not invisibly sealed up in the wall.  So "it" is probably either at one end or the other.