When I check the pressure on my horizontally installed expansion tank, I get a little water coming out as I depress the pressure gauge on the valve. The valve is on the lower side of the tank. Is that normal? I have a Watts PLT-12 expansion tank.
You need a new expansion tank - regardless of the install direction, water coming out the air valve is a sign that the internal membrane, diaphragm or bladder has failed.
Some tanks claim to care about install direction, some claim to be fine in any direction - get one that is either specified for the direction yours is, or any direction, or re-plumb to suit the direction of the one you get. Yours appears to be "any direction," as the instructions show vertical up, vertical down, and horizontal as options.
A typical water expansion tank has a rubber bladder inside to keep the air separate from the water. Such a tank will have a ring (protrusion or uneven line) around the middle of the tank where the bladder is attached on the inside. These tanks can be installed in any direction.
In the olden days, an expansion tank was just an empty tank and contained no bladder. The water remained down low, the air remained on top. The water entered and exited the bottom of the tank. Such tanks needed drained yearly because the air would enter the water and eventually the water would fill the tank. Emptying the tank and letting air back in fixed the problem.
Expansion tanks with bladders are much smaller than tanks without. So much so that it is cheaper to purchase a tank with a bladder and expansion tanks without bladders don't exist any more unless in a heating system where the water runs out of oxygen to create rust.
I looked up the Watts PLT-12 expansion tank. In certainty, the bladder in your expansion tank is busted and you need a new one. Water does not smash. The purpose of the expansion tank is the smashed air creates a constant pressure on the water. It also keeps your well pump from short cycling (on/off all the time) every time you use water which will shorten the life of your well pump.