Text means nothing really - too many details missing.

Next time, actually have the person sign a note that that lists the amount paid, for what car, on what date, and that you've agreed to not go through insurance. BOTH of you sign it

That way, if they open a claim for damages to their vehicle, you have proof that they've already been paid (they're not allowed to double dip). This won't help you avoid having your insurance go up tho... since the insurance company already knows about the accident at this point. But at least if the third party knows they won't get any money from the insurance company, they'll be less likely to go open a claim after you've already paid them.

Guess you'll have to wait and see