Hmmm I don't know if this is similar.
But I got up and played yesterday. My XB1 usually updates automatically. So I was doing my daily 5 radiant quest (my guy is lvl 115 and the main quest are long gone). And no quest were happening for the DLC.
I then checked my Fallout 4 installation and my list and didn't see the Automatron stuff. I then hit the manage option and the Fallout 4 DLC was ready to be installed.
I had to do this for both of my XB1's. Which is really weird as they usually automatically update and install everything. Including the patches for Fallout.
I would of thought it was glitched, but I actually had to click on it to install the DLC. Hopefully our problem is similar. Just manage the download and then it will show an option to install your season pass, Automatron DLC.