With rated games, if you have a subsciption, it will always be the full set of expansions you are subscribed to. If you have no subscription, you can make a coarse selection between "Only base game" and "Prefer expansions"/"Wait for expansions", in the auomatch panel of the "Matching" tab.
If you automatch unrated, you can fine tune which cards you see using the "Familiar Cards" tab, where you can declare whole expansions familiar/unfamiliar to you and go down to the card level as well (cards in color are familiar, cards in greyscale are not).
If you automatch unrated, the card pool is restricted to what all players consider familiar cards. There is one additional option relevant there, which you can find in the "Options" panel: "Max unfamiliar cards". It's 2 by default, meaning you can have at most 2 unfamiliar cards in your kingdom. You can set this to 0 to not have any unfamiliar cards at all.