Increment, delay, and why your first rated game feels fast.
The number that matters
A time control like 15+10 means fifteen minutes for the whole game, plus ten seconds added after every move you make. The increment is not a bonus for playing quickly; it is there so that a good position is never lost purely to the clock.
Three habits worth building
Press the clock with the same hand you moved with — it is a rule, not a courtesy. Write the move down after playing it, not before. And when you have under two minutes, stop writing entirely: the rules allow it, and the time is better spent on the board.
Why the first rated game feels fast
It is not the clock. It is that you are checking things you normally take for granted. That settles after three or four games.