From what I seen.
Say you are a rook and the city at strats was 100%. You attack a say a knight field and take the base with their city at strats at 50%. Downtime even through the switchover is still the same as if it were under knight ownership in this case it would be down for about 120 mins.
Yes, when your country takes another ones base, you get the downtime that existed before it was in your possession.
With cv base takes, sometimes it is very important to resupply town from the ship, I've seen downtimes of over 100 minutes remaining on the WF after we captured a base.
Of course if this happens to you, and they don't resupp, let it cool, sneak in, deack, and retake.
