I looked at the schematics (block diagrams, actually) last night and saw much of the same.
Pushing the ABORT STAGE button arms the pyro system (if MASTER ARM isn't already on) and fires the helium, fuel and oxidizer pyros to pressurize the APS (if they haven't already been fired). It also sends a signal to some electronics (or relays) called the CES but I haven't yet found the details for that device.
The CES in turn issues the actual staging command. First, four sets of separation pyros (one set in each quad) are fired, the interstage electrical circuits are interrupted (deadfaced) and an RC timer is started. After the timer expires, it removes power from the now-fired pyros and starts a second timer. When that timer expires, it fires the guillotine cutters.
The values of R and C aren't specified, but the text says both timers have the same period, 15-20 ms. That means the guillotine cutters are fired 30-40 ms after the separation pyros and deadfacing switches. There doesn't appear to be any way to slow down the sequence or to fire only some of the separation pyros.
So this still doesn't resolve the question of when staging actually occurs during the ascent sequence because we don't know what the CES box does. (Remember the ABORT STAGE button signal goes into that box, and the actual staging signal comes back out). But I'm inclined to think that staging does not occur immediately because there's a second switch, labeled simply STAGE FIRE/SAFE (and covered with a big bold switchguard) that would directly generate an immediate staging sequence, bypassing the CES, and if that's what they wanted they probably would have used it.
And if ABORT STAGE doesn't cause immediate staging, it's not clear to me what purpose is served by pushing it. The commander has already pressurized the APS manually by turning on MASTER ARM and flipping the Ascent He Press switch to FIRE after selecting one or both helium tanks. The fuel and oxidizer valves are fired at the same time.
Every time I look at these diagrams I'm amazed to see all those relays, diodes and simple transistor circuits and I'm reminded that pretty much all of Apollo looked like that. And I think of how unreliable an electromechanical device like a relay can be, and I can see how the designers went to extreme lengths to detect failures and provide workarounds. E.g., the actual pyro firing relays are all double-throw so that the pyro bridgewires are shorted until the relay operates. The pyro circuit does not share a common ground with the rest of the systems. Zillions of connections to the caution and warning system and to telemetry discretes are used to (hopefully) detect stuck relays and/or switches so that, for example, a stuck firing relay can be detected before somebody turns on MASTER ARM and fires a pyro unintentionally. A single "logical" diode is sometimes constructed from four diodes in series-parallel so any one failure (short or open) will not prevent proper operation. And of course just about everything is duplicated -- two sets of firing relay circuits, two explosive device batteries, two pyros on (most) valves, bolts and cutters, and so on. But there are still single points of failure that couldn't be detected until too late.
Although I would design this system very differently today, using modern technology, a lot can be learned by studying Apollo about anticipating failures, protecting against their devastating consequences (like a pyro firing prematurely) and providing workarounds. It's still relevant.