I think that all indications are that they reproduce parthenogenetically, precisely by getting wet. You are being thrown off by the fact that the other mogwai produced in Gremlins when water got spattered on Gizmo were much more mischievous and dangerous than their relatively mild-mannered progenitor. However, the in-universe reason for the difference in temperament seems to be that Gizmo is just a really, really friendly mogwai; more typically, the mogwai are not willing to get along with humans or serve as pets.
The out-of-universe reason that the later mogwai, created from getting Gizmo wet, were distinctly nastier, even before they turned into gremlins, is that the movie was originally going to be much darker. There would have been a lot more blood and violence, including Mrs. Peltzer being decapitated by the mogwai. There was no "good" mogwai (the name means "demon" in Cantonese) in the original treatment, and the original creature would have become the gremlins' ringleader, Spike. When the plot was changed to give the film a somewhat lighter tone, the personality of the progenitor mogwai was toned down, and the creature became the friendly, goofy Gizmo.
The second film features all sorts of new, modified gremlins (The New Batch was its subtitle), produced by the creatures consuming genetic modification serums in a laboratory. So the form taken by any creatures in that movie is not standard. Out-of-universe, the Gremlins 2 was only got produced because the makers were allowed almost total freedom to make the second film a spoof of the first.