The Black Cats signed the Welsh full-back for £2million from Scottish giants Celtic last week and he is expected to provide healthy competition for Jones who made most of his 14 Premier League appearances last season under the Dutchman.
Sunderland parted ways with French veteran Anthony Reveillere earlier in the summer and will now look to Jones and Matthews to fill the right-back slot.
"He played many, many games for Celtic, also European games," Advocaat told the club's official website.
"(Now) he must know the game, understand the game the way I like to play it."But it's good competition for Billy, who did really well from the moment I arrived."