'I get it' vs. 'I got it'
First of all, It's usually "I've got it". But that's just nit-picking.
Native English speakers usually use either interchangeably to mean the same thing, that is, they understand now. There doesn't seem to be a difference in meaning or usage due to the different verb tense.
They also sometimes add "now": "I've got it now" or "I get it now".
This is the usage to which I prescribe:
I get it now (that you have explained it more clearly)
I got it the first time(, there was no need to repeat yourself).
Most people aren't as particular, and will use the two interchangeably.