I'm pretty sure that the Fall of Gallifrey coincided with two events in Earth's timeline: End of Time and Day of the Doctor.

In DotD, the Time Lord war council mentioned that the "High Council were in an emergency session yadda yadda their plans have already failed": which I assume to be Rassilon's Ultimate Sanction. If this is true, then the events of DotD occurred simultaneously (if not within a short few days before) with End of Time and present day Earth. One point in Gallifrey's timeline was fixed onto two points in Earth's timeline; one during 10 and another a few "years" later with 11. (I wish I could draw us a "time chart" here, haha)

So we have the High Council in a separate chamber, enacting their dastardly plan while the Time Lord war council are alerted to the Doctor's presence and the subsequent theft of the Moment. And then they would have been notified of the theft as they go about tearing into reality.

It seems not all Gallifreyans wanted to end all existence to escape the Time Lock, just the High Council + Rassilon. The others just wanted to fight their War and hope to win. As events drew close to the last point in the Time Locked timeline before looping back, they agreed to the Doctors' cray cray plan and shunt Gallifrey to a pocket dimension.