Having used it from those early 1990s times of the new terminal, what I recall was Satellite 2 being only used for domestic operations; AirUK had then quite a trunk operation to Glasgow/Edinburgh etc, and I believe Ryanair started there as well to Ireland (Common Travel Area). It was always connected by a high level walkway from the start, so more a pier than a Satellite. Inbound passengers just walked straight out along the terminal building periphery, where there was a baggage belt, I don't recall a route for passengers to immigration/customs - all the early international flights I took were from the "real" Satellite 1, accessed by the Transit.
The operation went through various name changes every few years, from Air UK, which slowly got absorbed by KLM, was rebadged KLMuk, then the non-Amsterdam routes were renamed again as Buzz, and finally that was sold off to Ryanair.