There's good argument for and against jhin killing the elder, without additional information concerning the event and what transpired during the invasion itself regarding the elder's fate we can't really know. Killing the elder isn't out of character for jhin, we know that he targets artisans (jyom pass), musicians (sona) and other martial schools (wuju) - artists of any kind, really.
The crux of the problem assuming that Jhin killed the elder is the wind technique and the time line. We know that Jhin is a genius, capable of learning a wide and varied plethora of skills at a rapid pace from what the monks were able to observe from his time in Tuula prison. I think that he definitely has the capability to learn or at least mimic the effects of the style. But we also know that Jhin was likely imprisoned before or even during the noxian invasion, which gives him an alibi and renders him incapable of committing the act.
But if Jhin DID do it, you would have to ask how he got there, what his motivation would be to kill the elder, and in that specific way. Assuming he was safely imprisoned during the noxian invasion and tucked away for what we can assume to be years it seems unlikely that he could ever escape unnoticed long enough for a murder. The chaos of the noxian invasion with so many hands rushing to fight the runeterran equivalent of Stalingrad, however, might have bought him the window of opportunity he needed to move undetected. Even if he was recaptured and incarcerated shortly afterward the window of time he could have had until that point may have been enough for the damage to have been done.
I would put the use of the wind technique down to artistic irony, using their own technique against them, which I feel is something jhin would consider doing with his strict attention to detail. He may have decided to switch his MO to avoid being detected as the possible killer, something his intelligence is capable of, but I don't know if he is capable of breaking his vice for his own brand of artistry to do so. Something else that we do not really consider is that the killer does not know the wind technique at all, but managed to somehow deflect or redirect what we presume to be the elder's attempt at self-defense, making it seem like he was killed by a wind technique. This would probably put it beyond Jhin's area of expertise, given what we know about him so far, in-game and lore-wise, though. Just food for thought.
Further, we know that Jhin is not really familiar with Yasuo and does not know him personally like with Shen or Zed, so his motivation to cast suspicion on and dishonor Yasuo specifically is questionable and seems more likely to be an unfortunate happenstance for Yasuo than by design. It would strike me that if Jhin did kill the elder, the miraculous absence of yasuo during the invasion would seem like an extraordinary stroke of luck and an opportunity he could not ignore, as he strikes me as an opportunistic killer. It might also explain why jhin does not know yasuo further, never having the chance to have met him during that time frame when he was supposed to be there defending the elder.
Just my thoughts on the matter, anyway.