Is it typical for the front and rear gear levers to be reversed?
Gear shifting has historical lineage, not always "logical" or intuitive by modern logic as observed by newcomers to the activity. 

Originally, cables actuated the pulling of a mechanism, and release meant relaxing the tension, which mostly then let a spring return the mechanism to its lowest state. 

This translated to pulling = lifting/pushing the system up, against the gears, so moving the chain from smaller, up onto bigger sets of cogs. Dropping = the easier task of letting the chain fall from big to smaller rings, which the internal spring could handle. When indexed shifting arrived about 30 years ago it just aligned the clicks to a particular gear; then, first in mountain bikes, then road, the integrated levers made one lever for up, the other for down. 

The issue you're asking about relates to the fact that "bigger" gears up front do increase your gear, but in the rear they decrease, or lower your gear. The release of most thumb levers relaxes the cable, which drops the front to a lower gear, but drops the rear to a higher gear. 

With a few unsuccessful exceptions that tried to use the spring to push the chain onto bigger sprockets, this is still the general pattern - EXCEPT Now, I understand Electronic systems can be programmed entirely different, even mixing left and right signals front to back, an exceedingly confusing idea in my opinion. 

Learning to shift the traditional logic is easy enough to master in a couple weeks, so don't get worked up about something thousands have managed to cope with just fine.

Grip shifts are my preferred MTB choice, but again the tension/detension concept applies relative to which way you rotate the barrel.