I prefer to incubate my clutches. Each clutch can produce 50-200 baby snails just to warn you. It needs to stay moist but not wet. I find the easiest way to incubate is to take a very small tupperware container and put a single lightly dampened paper towel folded into quarters in the bottom. The fold two dry paper towels into quarters and place them on top of that. Put the clutch at the very top and tightlly lid it. You can then float it in your tank. Check it daily and remove condensation from the lid. If the towels get damp, replace them. They typically hatch at 8-9 days this way. When you notice that the clutch is turning blueish/greyish you can open it into the tank or a breeder trap. Typically after noticing the color change, they hatch within 24 hours and need to be able to get to the water immediately.
Your water level sounds fine. I was just concerned because it looks like it was laid in an awkward spot. A good rule of thumb is to drop your waterline as much as the largest snails diameter.
And you are correct, Mystery snail is one of tons of different species of apple snails. Its formal name is pomacea diffusa. They were previously described as pomacea bridgesii which is where the brigg came from. They were adn are commonly called brig snails and many of us are stubborn about changing our ways and actually calling them diffusa, lol.