The arrow is useless because the instant the 2.5s expire, she is on to you. There's no time between the arrow telling you where she is and she hitting you, definitely not a time in which you can run away from her.

Literally every assassin buyes at least an item that gives mov speed, that + boots + mov speed from other sources means that every champion (definitely every assassin at least) runs at least at 410 mov speed out of combat. That's the bare minimum.

That mov speed is high on a champ you can't see. If I see a zed or a Talon coming from afar, I know where to run (assuming there's a way you can run to, that is), but I know where eve is only when it's already too late, you don't need much mov speed for that.

there is no way an Evelynn can proc an E on someone unless they were CC'd by someone else or she burned Flash.

It happens all the time, you probably didn't see evelynn enough I guess.