I guess you could say it started back on PeW with The Spirit Of Radio - the chorus is a sequencer that he triggered with his foot, I think...and then there's the sequencer on Vital Signs, which I think maybe was them playing to tape live?
They clearly made a decision after GUP that they would not allow their arrangement choices to be dictated by the binary "bass or keyboards" thing. We also should not forget that they actually brought a keyboard player in during the PW sessions. I think this has been downplayed over the years, but it's probably good to remember that a lot of the parts that were being sequenced were parts Geddy never played in the first place, and likely were beyond his skills as a keyboardist.
I think that time is an interesting period in their career...they really challenged themselves to replicate those arrangements live. One could argue that it was to the detriment of the live energy of the band - Geddy spending so much time locked behind the bank of keyboards, Alex married to his pedals. It's interesting to imagine what it would have been like if Rush were not so obsessed with recreating the album arrangements - what would some of those songs from PW or Hold Your Fire be like if they were more stripped down live. We'll never know. I personally never had an issue with the triggering of keyboard parts back on those 80s tours - but when they started triggering background vocals (I think beginning on the Presto tour?) that somehow seemed less authentic. It's really just semantics, but it seems like more of a cheat somehow.