In Bridge, go to Preferences->File types (or so). There you assign the tools.
Thank you for trying to help but I had already tried that and unfortunately it does not work with InD CC 2014 running on Mac OSX 10.8.5.
In this version, Illustrator is pre-selected as the Default application and there appears to be no way to remove that setting.
This to me is a major Bug because it is extremely inefficient to have to use a Right-click + Menu selection every time I need to re-open a Tiff or PSD when a simple click on Edit Original should rightfully re-open a file in the App which created it.
If you are on Mac: select any tiff file on your desktop or in any folder, then Cmd-I to read the informations > Open with… Choose Photoshop, and click on the “Modify all” button (I am not sure of the exact term since I work with a French system).
I have no idea what caused my setting in the Finder to change to "Illustrator" but it had indeed done so.
I have changed it back to Ps CC 2014 and that is now showing as the Default in InDesign for Tiffs and PSDs and they are all now opening in it accordingly.
Thank you so much for solving that for me!
Bridge has nothing to do with this. It's set by the O/S.