My Sublime Text 3 ( but also applies to ST2 as I experienced the same issue before I switched to ST3 ) requires restart for any settings changes to take effect. This happens on a Mac Mini in the office but not on my Macbook Pro ( which is pretty much the same setup ).
I do sync settings over Dropbox by symlinking Application Support/Sublime Text 3
folder to Dropbox. However, I can recall it happening even before I did that.
Any ideas how to make it apply settings changes immediately?
First, make sure you're running the latest build of ST3. Remember, this is beta software, and things break/change/get fixed again from version to version, so it may just be an issue with your particular build.
I suspect that this has something to do with Dropbox, as settings changes should be applied as soon as you save the settings file in almost all cases. For example, changing the theme should happen immediately. To test if it's Dropbox-related, unlink your current symlink to ~/Library/Application Support/Sublime Text 3
and make it a regular directory, then copy all your settings over and try to change something. If it applies right away, then it's an issue with Dropbox.