No Full Synchronisation Requirement
This Memory serves as the tutorial for the guild contract missions, in which (similar to Assassin’s Creed: Brotherhood) you send your students out to other cities on missions, which reward them with experience and you with money and resources. The major significant difference is that you can attempt to wrest control of a city from the Templars, and reinforce it with your Assassins as a permanent source of income and bomb materials. The best way to train up your apprentices is to send them on the missions which feature the city name in them, for example the compulsory mission of this Memory - Bursa's "The Little Prince". These missions offer high reward for little risk, so make use of them as they are not repeatable.
In this case, simply send your apprentice assassin on “The Little Prince” contract mission in Bursa by selecting them following the on-screen prompts.