I just saw a Yasuo ulting off Quinn's E

It's a knockback, which yasuo can also ult off.

It's a displacement. Yasuo can ult off of any displacement ingame (knockups, knockbacks), e.g. Quinn E, Trist Ult, Shyvana Ult, Syndra E, Draven E…

That's lame, so Quinn's ability screws her but when Trist jumps she is immune. Does cait's net trigger his ult?

Is it a bug or intentional, because that is hardly a knockup...

It's intentional, and it's not a knockup.

Yasuo's ultimate actually states that it can be activated on any target within range that is Airborne. Airborne is a status effect that happens when someone is affected by knockup, knockback, pull or fling effects. All of those cause the target to be Airborne.

Quinn's E has a very short knockback, specifically for the interrupt effect.

Quinns e has a small dispalcemtn attached with interrupts channeled abilitys. Yasuo's ult can proc off any displacement so makes sense but it is such a short time frame he would have to be spamming it.

yasuo can use his ult when a champion is airborne quinn e knocks a champion into the air thus yasuo can use his ult when an allied quinn uses e i don't understand why everyone is always so surprised to learn that this applies to every single knockup. rek'sai isn't even out and i know yasuo can ult off her unburrow, yet i know people will be posting for months that OMG YASUO ULTED OFF REKSAI BURROW OP

Last time I checked (just after Azir came out), over a third of the champions in the game had at least one ability that Yasuo could ult off of.

I'm pretty sure you can use yasuo ult when Aniva smacks people with her wall.