The way it works is, at least on my Gsync monitor (144hz, but supports 120hz, 60hz, 30hz and 24hz) is, the driver (should) implement Vsync and the game itself has Vsync disabled in software (which is the correct implementation, for those of you w/o one of these). So if your monitor is set to one of the above Hz, the game will never exceed this framerate and will be smooth and tear free anywhere where the frames are between its bottom level (there is a floor on this where Freesync no longer works, but shouldn't be a problem for a console, Freesync 2 addresses this issue, I believe) and the cap of your monitor setting (144hz is common, but could be set to 60hz if you so chose). The problem I see here is, the XB1X doesn't have software to set the monitor, so this will have to be done by the console automatically. They may choose 60Hz... we'll have to see, or more likely, this will be selectable in the XB1X settings under the video options, assuming they have the OS detect your monitors capabilities. But the point being, the frames will never exceed your monitor's hz setting (when setup correctly).
Also, by doing this, typically a game will gain average frames per second... so a higher framerate, higher framerate average and higher lowest framerate, without tearing, up to your monitor's Hz setting.
And just to add, just b/c your monitor is running at 144hz or 120hz or 60hz, doesn't mean the framerate needs to be that high, w/ freesync the game could run at 36 fps and vary up and down between 30 and 60 on a 144hz monitor, but the point of freesync is that it will run at a higher framerate by default and be as SMOOTH AS BUTTER w/ improved input response and no visual tearing, no matter what FPS the game is running at.
My guess is you will select the resolution and Hz settings in the video settings of the console and this will hard cap any game at that FPS as the upper limit, but it will be unlocked up to that point. So games that are set to normally run at 30fps will vary between that and your set limit, not that you will be able to tell, at all... it will just be smooth, jitter free w/o tearing and you will get the input response improvements as well (not to be undersold, as I don't see that mentioned but is definitely a benefit).