Jhin Team fight Help?

I main support but I decided to try other roles as support isn't always available. I know Jhin is marketed as an ADC so I tried playing him as such. I've gotten better at cs'ing with him and I learned how to hold lane well but when it comes to team fights I suck! I mean I practiced a lot in bot games or custom games to get better at cs'ing and 1v1 or 2v2 or 1v2 duels. But bots never really make good team fights. They're too predictable and rarely jump you at the same time unless you're alone in their base. I have no idea what to do with Jhin in team fights. For one getting Jhin to the team fights is hard... Jhin is an exceptional slow champion so when the team fights start in mid it's a dangerous trek for me to go through the jungle alone to reach mid. Sometimes the enemy jungler would just jump me then. Recalling and running through mid is too time consuming. Second issue I have is... What to do once I got in range. My team said I needed to help in team fights so I tried. I attempted to just ult when I was in range. But apparently that's not good enough even though I helped my teammates run away better during a fight or I got an assist for helping someone kill. When I tried getting into the fight... Jhin (from my noob POV) is highly dependant on his auto attacks to do most of the damage, no? Problem is most champions' ability powers out range Jhin's auto attack range. So if I'm close enough to do 1000+ damage, you're also close enough to stun/root/etc me. Majority of my diving into battle attempts ended with me dying within a second. When I use my abilities I barely make a dent. When I attempt to stay in the back and fight... Well my damage output decreased dramatically.

That game we lost but there were a lot of other factors that contributed to the loss... However those factors are irrelevant as I've seen strong junglers or adcs or Nasuses carry the game regardless of how bad their team was.

I'm seriously confused as to how to use Jhin during team fights. I know it's obvious not to ult in the middle of the team fight and keep track of my reload. Or maybe I don't know how to ADC in general.