Correct. He gets paid on the days he's on the active roster. And he gets service time for the days he's on the active roster. So, for him that's when he starts. This is the same thing that happened to Daniel Ponce de Leon last year. He was a starter for several of those doubleheaders, and only on the roster for that day. He once spent more than two weeks with the Cardinals' major-league team, but he only earned two, three days of service time and two, three days of major-league salary. This could catch up with him at some point because service time determines Super-2 status or arbitration rights (and it's also something that is used in arbitration hearings).
The Cardinals addressed this in some way, realizing what all the moves had done for Ponce de Leon and his service time.
First, he's out of options this season, so the Cardinals did lose that flexibility with him. Second, he's making more this season than his service time would suggest. The Cardinals use an in-house metric to determine the salaries of players with less than three years of service time. They use WAR and they use service time. Well, they increased Ponce de Leon's salary and figured out that increase by giving him the service time in their internal formula for all those days he spent with the team -- while not on the active roster.
But, yes, Oviedo and Whitley and Elledge are going to see this same kind of thing this year.