Vic,
A wing generates lift in proportion to the square of it's velocity. So, when all other things are held constant the plane climbs when prop thrust and airspeed increase. Notice I said "proportional" not equal. The wing also generates lift in direct proportion to the angle of attack of the wing. Why am I bothering to mention this? We can use one to compensate for the other. Here's a common example. When landing everyone knows you have to steadily increase up elevator as airspeed falls in order to maintain a constant descent rate to touchdown. What you are doing is increasing lift with angle of attack of the wing to compensate for the decrease in lift due to falling velocity.

Designers use the same technique to automatically maintain altitude with an airspeed increase. Think of your Pilatus as a yardstick attached to the ceiling by a string. The string is attached to the yardstick at it's center of gravity so it is balanced level. If we tape a quarter to one end of the yardstick that end sinks slightly and the yardstick is no longer level. Downthrust in an engine is just like adding weight to the end of the yardstick. A prop with 0 degrees of downthrust directs 100% of the force horizontally. But if the engine is angled down at 2 degrees, about 0.1% of that thrust is straight down just like adding the quarter to the end of the yardstick. Even better is the fact that the downforce increases in perfect proportion as velocity increases. In a nutshell, we put some downthrust in our prop so that as lift increases in proportion to the square of the plane's velocity, it also decreases due to downthrust pulling the nose down and decreasing the angle of attack of the wing reducing lift. When everything is designed correctly there is no climb when speed is increased.