Abandon Ship was a very interesting drill, because we guys in the computer room would get to go outside. There were two phases to this drill. When I was a junior person in the division, I would go with my group to the exterior of the ship as fast as possible, and we would assemble on the starboard side of the ship, just aft of Talos missile launcher, where our assigned life raft was located. The senior person would take the roll and report the results to the Department Head, who in turn would report the results to Damage Control.
When I became more senior in the division, it became my job to remain behind and pretend to destroy the equipment, in particular to burn the contents of the crypto safe and to destroy cryptographic equipment. This meant pulling out the drawers and simulating chopping things up with fire axes—however, the equipment was very important and expensive, and I would not actually destroy it unless absolutely necessary. (The capture of the U.S.S. Pueblo in 1968 was always held up as an example of why the cryptographic equipment had to be destroyed.)
When I was done with the cryptographic equipment, I would join the division at their assembly point. Then the Department Head would be notified that I had joined my division and Damage Control would also be notified. (Usually the drill was over before I got to go up to the main deck, so I suppose that meant that I would have gone down with the ship.) Here is a link to the Pueblo story: https://en.wikipedia.org/wiki/USS_Pueblo_(AGER-2)