I may have misunderstood the question, so forgive me if I'm way off.
When either faction locks two pairings a city siege results. This can be done via domination (dom) locks or Victory Point (vp) locks. In the case of a dom lock, then the highest timer (bo or Keep) in the last pairing is your countdown as to when a siege will begin. In the case of a VP lock of the last zone of a second pairing the "countdown" may not be as exact. Unless there is a BO or Keep being taken that will give the last VP points needed to flip the zone. In the latter case the timer is likely three minutes (in the case of an objective that was just taken) or up to 15 minutes if the offensive force is simply having to wait for the last BO to become available before zerging it down and flipping the zone.
You will sometimes here people announce in T4 that a zone is locking in X minutes regardless of timers. This is either optimism, accurate prediction, or straight up propaganda intended to bring players to the zone to help lock it. You'll get a feel for which is the case based upon your own experience with both the mechanics and those who speak often in Tier 4. :)
Once a city becomes open to siege (contested) the city icon will show as yellow on the empire/chaos pairing map. A timer also shows. The clock starts at 60 minutes and counts downwards. This is the countdown for starting a new city siege instance or the time left to jump into a new one. This is also your countdown for finishing your existing instance so you can jump into a second one.
Once the city in question is no longer contested, one can no longer enter/start a new instance*. The city icon will switch back to the faction color (white and blue for good guys, black & red for muppets) and a new timer will appear. This count down shows the timer for the "rebuilding" phase. This is essentially the time you have left to finish your existing instances. Once this timer counts down the city status drops a point and the underdog points are tallied.
*there is a known exploit where people can crash their client while in an instance and get a new instance (often their third) even though the city is locked. I won't give the details as doing so is a sign of poor moral character and no one within our alliance should stoop to such levels.
I hope that helped.
Cheers