Well, that "another guy on saxophone" is actually a veteran on Philip Glass' ensemble; I have Richard Landry playing on some of Glass's early works such as "Music in Fifths".
Process music...yeah, that's a strange topic. I think you can trace back to the point where it forks off of minimalism if you look at La Monte Young's "Compositions 1960", although the inspiration for this goes back to John Cage and his own procedural methods. Young managed to strip down the idea of "process" to simple, koan-like fragments that delineate the framed procedure for the work.
It's interesting that this set of pieces came about after Young's studies with Karlheinz Stockhausen in 1959, because they're not exactly "Stockhausen-esque"...at least, not yet. Instead, Young was inspired to investigate Cage's procedures by Stockhausen, who was quite taken with Cage's methods and results at that time. Stockhausen himself wouldn't hit this stride until 1968 and "Aus den Sieben Tagen" after his own process-based methods grew to a massive level of complexity with "Kurzwellen".