I was having this problem on my Mac where every 2nd time I ran Garmin Express, it would relaunch the installer package. Really annoying. (I'm running OS X 10.10 Yosemite and Garmin Express 184.108.40.206)
I guess it does this when there is an update available, would be nice if it actually told you that's why it was running the installer again.
I googled around and found the following solution:
1. Open a Finder window and from the menu bar, Go -> Go To Folder
2. Enter ~/Library/Application Support/Garmin/Express/AppUpdates
3. Delete GarminExpressInstaller.dmg
It won't bug you again until it downloads the update installer again... if you run something like LittleSnitch you can make a manual rule to ask for permission to connect to download.garmin.lfs.netdna-cdn.com if you would prefer the process to be manual
The most annoying thing is it makes you reboot your Mac after the installation.... very un-Mac behaviour...
It appears that the new Garmin Express 4.0 installer doesn't require a reboot so that's good