Back in the day, when Phil, Mike, and Tony was up on stage doing that particular tour’s/album’s current material, was there a contractual obligation to perform ONLY Genesis material…or could Phil slip in “In the Air Tonight” or Mike do “The Living Years”?
This is probably not exhaustive, but I don’t see either “in the Air Tonight” nor “The Living Years” on any of the concert set lists archived by setlist.fm.
Now, was that contractual? I don’t know. It would seem kind of odd to me, though, to hear a solo work at a band’s concert. If I did, I think it would be some sort of surprise encore number.
In the concert film Stop Making Sense, the Talking Heads take a break while the Tom Tom Club performs.
When we saw Eagles a few.months ago, they played “solo efforts” by Don Henley, Joe Walsh, and Vince Gill, as well as several James Gang songs.
I saw Tom Petty and the Heartbreakers here in Chicago in 2008. Looking at the playlist, about half of the songs that they did were from Petty’s solo albums (though, members of the Heartbreakers had played on those albums). They also played “Handle With Care,” a song from The Traveling Wilburys, of which Petty had been a member.
When I saw Electric Light Orchestra play live in 2018 and 2019, they, too, played “Handle With Care,” as Jeff Lynne had also been a member of the Wiburys. In the 2019 show, Dhani Harrison (George’s son) joined ELO on stage for that song, in tribute to his father.
(I should note that, at this point, ELO is pretty much Jeff Lynne with a touring backup band, so he could, in theory, play whatever he wants. 
)
Getting back to the Genesis question, what I would be more curious about is if they played songs from the band’s Peter Gabriel / Steve Hackett era of the band, or not, as I could see that possibly being more contentious than playing things from Phil’s solo albums (or, for that matter, from Mike & the Mechanics).
Genesis definitely played earlier material in concert after Gabriel and Hackett left. I saw them several times in the 80s and remember them playing a lot of older material. I even saw them play “Supper’s Ready” once, which was awesome.
My experience coincides with Shoeless.
There are a lot of Gabriel era songs on Seconds Out, their first live album after the split from 1977, including “Supper’s Ready”. It’s a very good album, and Phil Collins REALLY could channel Peter Gabriel’s voice hauntingly well.
And the extended version of “I Know What I Like” was always a crowd pleaser.
To me, that kind of makes more sense, as it’s a Genesis concert, not a Phil Collins show or Mike & The Mechanics show. When a band changes singers, I think it’s pretty usual to keep the old songs in the rotation, no? I mean, Van Halen continued to play their David Lee Roth songs after replacing him with Hagar, and I’m pretty sure AC/DC didn’t stick to new material when Brian Johnson joined the band.
No, AC/DC of course never did, though it’s still kinda grating to me when I hear Brian Johnson sing a Bon Scott song. I dunno, maybe it’s because AC/DC with Bon Scott was one of my first favorite bands when I was 11 and Bon Scott was my first REAL rock’n’roll dead (I was aware of Elvis’ death, and then some more of John Lennon’s, but those were from the past,and Bon was MY discovery).
Something else that may factor into the Genesis performance question: I believe while Gabriel was in the band, all of the compositions were credited to the entire band. After Gabriel left, you started to see individual songwriter credits on the songs. As far as I know, Gabriel had no issue with the band playing songs he may have written while he was in the band, but probably couldn’t have done anything anyway since he wasn’t credited as the songwriter.