If you saved a file as 2015, that's what it will stay, but if you are saying that double-clicking on any file opens it in 2015, that's just an OS preference to use the latest version. If you have CS3 loaded, just open it first, and then do a File>Open, and they will open in CS3. If you have a shortcut or Alias to the program (like the one in the Dock in Mac OS), you can drop the files onto the alias/shortcut, and they will open in that version.
Any files that were created in CS3, and never saved with CC2015, will still be openable with CS3.
Any files that were saved with CC with have to be saved as IDML in order to open them with CS3, and then opened in CS4 and reserved as INX. Not a great workflow, but your only option for any files you saved into the new version. (The link below should get you a month free trial to CS4)
Sounds like you are on a Mac, which has no functionality for displaying version icons the way Windows does, so displays the icon for the most recent version installed, whatever the files really are. As above, unless you actually saved a file in the new version there is no change to the file.