To conform with Microsoft rules and regulations, you will now need to set the account that bought the "A Rift in Time" as your home Xbox, log out of that account and then log in to the account you want to play the DLC on.

Or alternatively, keep the account that bought "A Rift in Time" signed in and also sign in on the 2nd account to play there.

Here is some info on how to designate an account as the "home Xbox". See the "Switching your home Xbox" topic for details.