The Gods

The weak tribe has their own know-how to survive the turbulent period when titans around them fights against each other.

They rely on Bolghar protection and obey Bolghar words because the Bolghar tribe could protect them.

It is not that Bolghar tribe rules then and have no responsibility towards them

The Bolghar responsibility and duty toward the small and weak tribe around them is to protect them

As repayment for that duty, the small tribes would give offering of sheep's, resources and when war came, their warriors would listen to the orders of the Bolghar.

They are not vassals like in Europe medieval kingdoms but close to it.

Because some tribes could just go up and rides to different part of the Steppe if they wanted to .

Now, that the Bolghar could no longer fulfill their duty, the answer for these weak tribe is simple. Since you are now weak, we will rely on the strong.