Do you have Viking Invasion? If you do, then the more troops are in Kazar when the Mongols arrive, the more Mongols there will be.

Also, bear in mind that the Khan arrives without any adult heirs. (I don't know if he has any little kids) So if you get a chance to kill him early on, then you will be dealing with rebel Mongols, who are easier to cope with and may well be worth bribing.