Ok, the time dilation makes actually sense now. So like chemical reactions depend on temperature and pressure, physical reactions (if they can be called this way) are dependant on gravity and velocity (dependance on the last I can not quite get still). By physical reactions I mean the transitions between the ground states that time is defined by.

Sure, local velocity at any rate. If someone goes past you in a rocket, you'll notice that their Caesium radiation is oscillating slower than yours, so their second will appear to take longer than yours.