This is more than just "what is intuitive". It is an important convenience issue if you are trying to enter if the door is unlocked but closed and you have your hands full - elbows work great for pushing a handle down but not for pushing a handle up. It is also an accessibility issue - in fact the switch from knobs to handles has been great in general for accessibility and this would be a step backwards. And most importantly, this is a safety issue - if you are inside and need to get out quickly due to a fire, you should be able to rely on muscle memory to push a handle down just like all the other door handles.
My hunch is that this is a left vs. right issue. This lock is currently set to open on the left side. With the handle facing the right, it should turn clockwise to open and instead it is turning counter-clockwise. If the lock were to open on the right and the handle facing the left then counter-clockwise is the way it should turn to open so that it opens by pushing down.
It is possible to design a lock to work both ways. It is also possible to design a lock so that there is one model for "open on the left" and a different model for "open on the right". One possibility is that the opening direction is set in the handle itself, since you will normally want one handle (inside or outside) to open clockwise and the other to open counter-clockwise. In fact, this very similar if not identical model available from Home Depot Pro has installation instructions which include directions for reversing the handles. The pictures are a little confusing because they imply that you initially installed them to have the handles sticking out in the opening direction, which would never make sense, and want to switch to stick out in the other direction. But my hunch is that if you have them "upside down" this would switch the turn direction as well.
