What exactly happens during a Dragon Break?

Time more or less gets [censored] until Akatosh send in the Jills to fix it.

I'm not sure Akatosh can send anyone to fix it; he's the one that's broken, after all. The jills are more than likely an in-built feature of the Mundus that activates semi-automatically. That said, I have no idea how that would work.

As for what happens in a Dragon Break? There is written history during the dates of the First Era Break, and the Tiber Wars ended while one was going on, so it's not like history stops. It's just that history quits going in the same direction as it did before. Instead of going forward, it is free to move in any direction it likes. Maybe.

Linearity and causality temporarily absent themselves from the building. Their smiling, well-behaved darlings inevitable leap on the opportunity and throw/don't throw the best/worst party the untime's seen since tomorrow. Eventually, they piss off the neighbors and the cops arrive; by now, the partiers are giving birth to their grandfathers, burning down sheds they haven't built yet, and generally making a mess of things. Draco 911 clamps down on the scene until L and C return, after which everything reinstantiates into a coherent orderly worldline (with only half the vases shattered into pieces and a few topiaries remaining conversant in Ehlnofex).

Everything, all at once.

One dragon: broken.