I don't know if anything covers the away cup games by default.
Cup Direct always used to just cover the home games so that season ticket holders didn't need to faff around going down to buy their seat when it could be done automatically.
Away direct used to cover the all-ticket away games we got, again so that regular away fans didn't need to keep going down for tickets for the big games, and basically making it easier for the ticket office staff when we played the likes of Huddersfield, so if the game was made all ticket for us in the Cup it would cover it, but only then.
I'm saying used to because I've not been in either since I moved to Scotland, it might have changed since but better you doubt it now than get to the day of the game without a ticket because you're still waiting.