Is there a rule that doesn't allow adjustment during the opponents time? While playing a tournament, I adjusting my pieces several times during my opponent's time. He claimed a win for the same. Can anyone explain how this rule works and why is it there?
I think this FIDE rules section explains that:


  Article 6.2
  
  d. Only the player whose clock is running is allowed to adjust the
  pieces.


According to Article 4.2, a player should announce "j’adoube" (I adjust) before adjusting pieces on the board, providing only the player having the move may adjust one or more pieces on their squares (i.e. player in turn with clock still running).

In actual games usually the arbiter only issues verbal warning about adjusting pieces only in respective player's turn. But keep in mind you should avoid distracting the opponent, i.e. obstructing their view on the board when it's opponent's turn to make a move, since Article 4.8 applies if a player decides repeating disruptive behavior from his/her opponent, without announcing to adjust the pieces first:


  A player forfeits his right to claim against his opponent’s violation
  of Articles 4.1 – 4.7 once the player touches a piece with the
  intention of moving or capturing it.


Related issue:

Adjusting in ones turn only