If an enemy (rebel) ship knows where the PCs ship is heading on its hyperspace jump and follows it, when the enemy ship emerges into real space how, and how quickly would any sentry Imperial fighters be able to identify it as a rebel ship?

Would the rebels manage to get a few shots at the PCs ship, be identified as rebels, and then escape by jumping back into hyperspace?

Story driven, there is no mechanical answer.

Like 2P51 says, it's largely story driven. But I would lay down the following presumptions:

• Unless the Imperials just happened to be in a very fortuitous spot (narrative driven luck, so maybe only if as GM you really need it to move the story forward or if the PCs, who I assume are at least Imp-neutral, spend a light side Destiny Point to request it), the distance between any Imperial patrol and the hyperspace drop-in point will probably be Extreme range. Maybe Long range if it's patrolling an entry point for a specific hyperspace lane that the other ships involved are using. I would assume any Imperial patrol would have at least one ship, maybe a scout, with a Sensor range of Extreme so as to be watching for hyperspace ingress.
• The Rebels are unlikely to be operating Imperial-mandated transponders. Therefore, they'll show up as unidentified contacts. Even if the Imperials don't identify them as Rebels by ship class (a squad of X-Wings, a Mon Calamari ship) they're going to assume the Rebel ships are at least criminals and will close in, pursue and challenge over radio.

From there, I'd say it's just how long it takes for Imperial ships (likely, nimble TIE Fighters firstly) to close the range bands to the Rebel ships.

I want to say that would take three maneuvers (two to go from Extreme to Long, one to go from Long to Close) if the TIEs are already in space and gunning it to top speed. I'm not totally sure about that. But if so, I would say it would take three turns. (They could cover the distance in as little as two turns but I personally would presume the pilots would be canny enough to come in flying as Evasive Maneuvers until they're in weapons range)

If the players aren't also wanted by the Imperials for any obvious reason, they could also take their ship right to the Imperials and accuse the incoming ships of being Rebel privateers.

How long it takes the Rebels to go back to hyperspace is entirely narrative driven. Me personally, I'd say no less than three turns, for dramatic purposes if nothing else, and easily more like five or more. Though by the time the Imperials close range, even if the Rebels haven't left they'll have other things to worry about...

As a GM I might roll a difficult computers check for the Imps. Using success and failures to make their scan fast or slow. Depending on how the story was unfolding or if the PCs rolled a bad astrogation check then maybe they drop in close to the Imps and maybe all ot takes to ID them is a simple perception check. There are a lot of variables to consider, but as the others have posted it should be story or narrative driven. Personally I would roll behind the GM screen even just build the suspense and give the PCs that "oh crap" moment. But that's me and I'm a bit mean.

Great ideas pi3orionis and CMDR Canum. Thanks.

Arriving close to Imperial troops is an excellent way to spend Threats rolled on an Astrogation Check.

Story driven, there is no mechanical answer.

Technical a sensor check is simply a computer check, takes on round and if the ship shows up on the scanners … well … it still depends on the story what kind of transponder codes the rebels are using.

No transponder code: The imperials know immediately when they detect the ship that something fishy is going on, but have no way to be sure that it is a rebel ship.

Code, which is clean (stolen or otherwise): Move along citizen, we have no interest in you.

Code which is linked to a known rebel ship: Well, it literally announcing to every ship in sensor range that it is a rebel ship. Go figure.

The whole system of transponder codes, the bureau of ships and services (BoSS), etc is en detail in Fly Casual. SM has furthermore an easy 2 hardpoint mod which can change the transponder code and engine signature on the fly between predetermined IDs.

Personally I would roll behind the GM screen even just build the suspense and give the PCs that "oh crap" moment. But that's me and I'm a bit mean.

More importantly, your players are not well prepared

Thanks to our "Master Jedi" we are switching transponder codes AND engine signatures on regular base. That "Oh, crap" feeling comes for us each time we see another VCX-100 in our system … our GM is mean too and we can not be sure that we run per accident into the ship which ID we have stolen. ;-)