Did anyone also notice that the RPM of the engine increases (not much, but you definitely can hear it) when you put the automatic gear in "P"? Anyone knows how this comes or why this is?

 

What you're really trying to ask is why do your RPMs drop when you put your automatic transmission in gear; most automatic transmissions act this way, it is totally normal.

As for the "why", when you move an automatic transmission from Park (or Neutral) into any forward or reverse gear, the transmission is effectively hooked up in a gear and that stops one half of the torque converter; since one half of the torque converter is now stopped, it causes a fluid drag on the other half of the torque converter, and that extra drag is what causes the RPMs to drop. Take it back out of gear and put the transmission into either Park or Neutral, and the RPMs will go back up to the free idle speed.

 

Thanks, shipo, for your elaborate and professional explanation!