From the Help FAQ (scroll down to Players):
"We track service time in days. It is viewable by hovering over the ML Years value on a player's profile. Each day a player is on the big league roster during the regular season (even if he's on the DL), he accrues a day of service. In addition, we track the # of days a player is on optional assignment on a minor league team. If a player is on optional assignment less than 20 days during the season, this total is added to his big league service time. At the end of the season, if a player has 172 days or more (including any optional service days < 20), he is given a year of big league experience. If not, the days roll over into the next season. These years are what dictate arbitration eligibility and free-agent eligibility."
So, what you need to count is 20 minor league DAYS.