There are a few different ways to do this. Either wait until 17 and import the player that becomes fake and you keep his correct stats and whatever his service time is.
Or sim seasons with a player to get service time and stats close as possible. For your Tigers you'll need to do this with guys like Jim Adduci and Brett Pill. With Juan Carlos Perez you can import his fake player (He'll become generic when 17 comes out using a carryover save) and he'll keep his correct stats and service time.
You can also find a CAP with close enough stats then just sim a season to get correct service time.