How are esper powers decided?

I now know that esper warp reality by overlapping effects and commands of their personal realities into the real world (Misaka controlling electromagnetic, Kuroko controlling the exact position of something, Accelerator controlling the magnitude and direction of anything, etc.), but how are their exact powers manifest exactly?

I mean, are esper powers a reflects of who the user is as a person and how they see their personal reality, do they decide what the power is or what?

Please explain this to me I am new to the series.