Turrets, how do they work??

I've been playing since season 2, I have a pretty good idea how turrets work, the missile speed, dmg, etc. Although recently, the last few games I've played, totally crushed what I thought I knew about turrets.

The range, firstly, I'm not sure if turrets have a 'dragging' feature which enables them to get a final shot off before the shot is cancelled, but if so I would like to know that range because sooooo many times it's work against me, although few in my favor.

The argo, okay so this triggers me hard. From what I understand, if you are under an enemy turret, and you damage said enemy under said turret, the turret will prioritize you. Whether that has change or been slightly modified i'm not sure, but as an example: if I'm under a turret, and someone kills me under that turret, the turret should agro the champion who killed me correct? Because the champion who killed me would've had to been the last champion who damaged me (they got the kill) and that's what the turret priorities. My previous game, the game that tilted me enough to make this post, that didn't happen. A Jayce dove, ignited/killed me, with Leona tanking all the agro the whole time.

Now most likely I'm just uninformed but if someone could clarify I would really appreciate it.