Imagine a simple reaction game. on iOS touch device.
I set a texture to change color signifying it's time for the player to respond.
How do I exactly measure the time of the touch from the time of the display of the "go touch the screen" signal regardless of the frame rate of the app?
You can only get input in a frame. There is no exact timing(*); the lower your framerate, the less accurate timing is. If you're not taking pausing into considering, you can just store the Time.time when you like, and then subtract than from a later Time.time to get the delta. If pausing is coming into play, then you probably just want to add Time.deltaTime, every frame, to a variable that starts at zero.
(*) FixedUpdate is an option, but it should only be used when your input is directly related to physics. If you put too much in FixedUpdate, or make fixedDeltaTime too low, then the concept of FixedUpdate will become meaningless because there won't be enough horsepower to keep the higher framerate up for anything.
Just make sure your framerate is good. People don't sense time very meaningfully at the 30-60 fps level.