So in the movie, about a week after Cal is brought in (I did up a timeline which is the last link on my page on the lefthand side, and it is spoiler heavy because it goes into detail of what happens while he’s held there), Cal actually manages to break the Animus once the Apple of Eden is found in the memories of his ancestor. Idk if you’ve seen, but there’s an all new Animus, and it plugs directly into the brain stem via an epidural, and Cal manages to, like, breaks its hold on him In a weird way. At that point, the man who runs the facility, Alan Rikken, orders a purge on the facility and evacuates all the staff, including his daughter, Sofia, who’s the one that’s been working with Cal in the Animus.
At that point, the Subjects who have been in the Animus and are being held there escape the facility to fight back against Abstergo. So it isn’t so much that there’s a mass breakout so much as the facility is set to be purged, leaving everyone except the staff to die, so they just escape.