Too wet. Needs to dry until it is very near the same colour as it was before you wet it. Wet leather won't hold or give good impressions. Also when you fold leather, it will lose some definition as the surface is stretched. And folded wet will do worse. Your tooling should leave nice burnished marks, nice medium to dark brown.
For thin leather, glue it down to hard board, plastic or something similar to keep it from stretching. Rubber cement works well. It will peel off. If you do a search here, you'll also find that some use shelf liner with a sticky backing. Peel and press it on.
Shouldn't need to hit it more than once. Sometimes the stamp bounces and doesn't stay exactly in the impression, so loses definition. Professional stamps leave a cleaner impression, but the lower cost tandy stamps should still look reasonably good, and are good for beginners ... until you decide to get really serious about leather.
Tom
Edit: Rather than too wet, I think it is too dry. Do some test on a piece of scrap so you can see how it behaves versus the moisture content. Test stamp it every 15 minutes. When it is getting close to the correct moisture content, try every 5 minutes.
If it won't take impressions, it is too dry. If the stamp just about cuts through or does cut through, too wet and maybe too heavy a hand on the mallet.