The Main Campaign progress unlocks in the following manner -

1. Thuc Phan
2. Qin Shi Huang
2. The Scribe (Economic Campaign)
3. Genghis Khan
4. Toyotomi Hideyoshi

The DLC can be played at anytime, if you have downloaded and installed the appopriate DLC.

The Scribe/Economic Campaign is unlocked after completing Thuc Phan Campaign. After unlocking this is not linked to remaining Campaign progresses.