When my serpentine belt broke three times the problem was diagnosed as the power steering pump. Why wasn't this diagnosed when the tensioner was replaced. I am now replacing the power steering pump and the fourth serpentine belt. I feel I didn't get the service I previously.  My car is a 2002 subaru outback.

2002 outback does not have a serpentine belt, It has two drive belts and the power steering pump is on the left side with the alternator. The idler is on the right side which drives the a/c. The power steering belt is adjusted by tightening the alternator, so if only the tensioner was replaced there would be no reason to check the power steering side..

That is a valid question, but you should ask the shop that worked on it. Also do you know that the power steering pump will cure the problem? This remains to be seen....You can check one thing though...Look at the belt/pulley arrangement from the side. any pulley that is not exactly in line with all others, and any wobbling pulley is suspect. Serpentine belts are far less forgiving of these items than were "v" belts.
Good luck