The corridor agreement was that only pilots who were nationals from the four powers could fly them, any aircraft type, commercial, private or military. As the Soviets did not use the corridors this meant just UK, USA and France. This applied to the end. It gave some issues for the likes of BEA who had various other nationals on the fleet. The Soviet ATC were very adept at picking up accents which sounded unlikely, or even those who did not speak by radio. Prominent UK TV entertainer Hughie Green, ex-WW2 RAF DC3 pilot, flew his own aircraft down the corridor, presumably expecting by his accent to be assumed American, but was picked up being Canadian, had to return by airline and get a pilot to fly his aircraft out.
Cabin crew were not part of this, and the corridor airlines, plus the various holiday charter operators who set up base there, typically ran with crews recruited locally in Berlin, who would do the bulk of passenger PAs, in German. UK holiday carriers like Dan-Air (particularly) and Monarch had longstanding cabin crew bases there.
In the last few years a competitive carrier called EuroBerlin emerged, an Air France-Lufthansa joint venture, which operated with leased Monarch 737s and UK national Monarch pilots.
My understanding was, in the jet era, that BEA/BA One-Eleven crews typically did one week details there, as described above, and Pan Am 727 crews did three month tours. The main Pan Am 727 base was at Miami, whence an equivalent fleet operated over the Caribbean (there were also a couple of Pan Am 727s in Vietnam/Thailand until 1975, operating military charters, likely done the same way). I don't know if Pan Am crews could do multiple three month tours in Berlin, one after the other. The 727s were periodically returned from their European base, which was Frankfurt, not Berlin, to Miami for major checks every few years, and could be seen at Prestwick etc occasionally ferrying to and fro. BA through-routed several flights a day from the One-Eleven's Manchester base to West German cities, and thence to Berlin, running the aircraft in a common pool, and did the same when twin turboprops came along.