Been having the same issue...then someone suggested going on to the main Origin website here https://www.origin.com/en-gb/store/
Just log in...search for Trespasser and but it directly through their site....then open your Origin and it should be there to download. If your Origin is already open when you purchase the DLC...close it down and reopen and it will be there for download.
This worked for me...hope it helps anyone else having this problem
EA ...you need to get this sort of * fixed...not cool when so many people have been waiting for this DLC :/