How can you say to a child not to pour water on you when she is taking a bath? My sister use the term don't wet me and it sounds off
Don't splash water on me! / Don't splash me with water! / Don't splash me! (if it's clear that water is meant)
If the water didn't reach you because you were far enough, you can say:
Don't splash water at me!
As for the verb to wet, here is an example of how it can be used when talking about babies/young children:
The baby has wetted/wet the bed (urinated in bed).
So, you are right. Your sister really doesn't mean "Don't wet me!"
My opinion is that a person is being splashed with water not urine. Water wets things just as urine does. I think it is still correct to say. Don’t wet me! When someone intentionally sprays you with a garden hose, aren’t you getting wet? In this instance “ Don’t wet me!” fits. I think your sister may be correct.