All skills while level synced.

[Hasrat]

I think they mean if let's say you get Copperbell Mines during Leveling Roulette then you will get a Mog Tomestone at the end for completion. The roulette itself doesn't give the reward, but getting the specific duty through it will.

Last I read here, someone managed to get a specified instance through roulette, and was not rewarded any moogle tomestones. You are rewarded only for queuing exactly for the listed duties.