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 Console, log out of that account and then log into the account you want to play the DLC on.

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

Here is some info on how to make an account in the 'Home Xbox', see 'Switching your home Xbox' tab.