You should get a warning sign about the arrrival of the Mongols very soon (in less than 10 turns). The actual arrival of the Mongols will probably be more 20 turns later.

The Mongols comes in three waves with around 10 full-stack armies. They arrive either north of the Caspian Sea (en route to Kiev), or near Yerevan (en route to Antioch), near Baghdad (en route to Jersulame).

Have a nice time fighting them.