Well, the only time at which he had those 3 items, he also had a Last Whisper (and a Doran's Blade and Boots of Swiftness, but those aren't really as important) and you had no bonus health or bonus armor (not that you should as Jinx) which means he was basically doing true damage to you.
This was also at 29 minutes into a 33 minute game that ended with
10/1/8 and you at 4/5/3
Unless he got pretty much all of his kills at the end he was simply much more fed than you.
As for being able to survive something like that, you need to never be alone. I can't know for sure that you were, but if your teammates could absorb the damage for you, you should be able to survive even with him being that fed.
Also, his ultimate is not necessarily a "finisher". The slow makes his ultimate really good for an engagement while your front line collapses on the enemy. By the time he gets to his 4th shot, there is a decent chance he will be able to finish someone off.