Okay, here's an overview of how the updater process works on OSX, and this may help you then figure out what is going on based on what you see in your folder:
1. You out the game in a folder, which we'll just call /TLF/ for the sake of brevity.
2. You then run /TLF/LastFederation.app to play the game.
3. The game downloads this xml file and looks to see if a newer version is available:
http://lastfed.s3.amazonaws.com/TLFUpdatesList.xml"
4. If there is a newer version available, it puts up the in-game button that lets you do the download.
5. If you elect to click that button and go through the updater process, then the game itself downloads some number of zip files (however many are new since your last update) into the /TLF/RuntimeData/updates/ folder.
6. The game then shuts itself down, and launches /TLF/UDA/ArcenUpdater.app
NOTE: If the latter does not launch for some reason, then the game files will have been downloaded, but not applied next time you run /TLF/LastFederation.app7. If you run /TLF/UDA/ArcenUpdater.app manually, or the game triggers it, then all it does is look in the /TLF/RuntimeData/updates/ folder, find all of the numbered zip files in there, unzip them, delete them, and then run /TLF/LastFederation.app
NOTE: Actually some of the files from the zip get put into /TLF/DB/ as a subfolder, and then those get further moved into /TLF/LastFederation.app/Contents/Data/ as a way to make it so that one download can easily serve all three OSes supported by the game. That then leaves you with an empty /TLF/DB/ folder at the end of the process, but this is just purely a minor note.To me what it sounds like happened in riadsala's case is that it got through stage 5 just fine, and then for some reason on stage 6 did not launch /TLF/UDA/ArcenUpdater.app. But then when that was launched manually, it did everything else fine. After that point it was updated, so just running /TLF/LastFederation.app from then on would be running the updated version of the game just fine.
Apologies for the length of this response, but I figured that a full explanation of what is going on behind the scenes might either help bring to light the problem, or reassure you that all is well with your installation, whichever turns out to be appropriate in your case.
Thanks for your support!