This could be simply a bad that may be failing due to some oil contamination. This happens quite often when doing a big repair and cleaning the drive belts.
There is not extra adjustments to the tensioner that you can do. To help find the cause I would recommend, with the help of a friend if possible, to spray some silicone spray on the belts when the noise is present and see if the noise goes away. If it does go away when sprayed then this would indicate a bad belt.
The next step would also be to remove the belts and run the engine for a few minutes and rev. it up and see if the noise is present. If it is coming from the belts or from a pulley the noise will be gone. Then you can hand spin the pulleys to listen to them and feel for any bearing noise from the pulley. It should be smooth and quiet when spun. It might be that you have both a belt and a pulley problem which is very common. It is also common for the tensioner to make noise. To check this, use a long screw driver and place it on or around the area and listen on the handle end and the sound telescopes up and many noises can be discerned this way.
I hope this is helpful. Please accept and best wishes to you on your repair. Thank you.
You can run the engine with the belts off with no damage to the engine as long as it remains within a short period of time. The belts run the alternator, the water pump, and the power steering so the main concern is engine overheat. The main thing to do is to not let the engine get above the half way normal temp range and to shut it down at this point. But we do this all the time at the dealer to see if the noise is gone with belts off to help us diagnose problems.
:) I hope this helps. I hope it proves to be something simple like only a drive belt.