So I don't need to do anything? Are they taking in account for the validator I delegated then?

Yes, your whole wallet is automatically staked to the same pool that you selected. (Technically, the stake address is encoded in all the addresses. That's why the second half of all your addresses – minus the checksum in the last six characters – is identical. Your stake at snapshot time every five days is calculated by the funds on all addresses with that stake address in them plus the rewards on the stake address itself.)