When did you start the game? There's a known issue with EMF+SWMH in starts later than, I think, 1217 or possibly earlier (basically whenever the Mongols don't appear off the edge map but are already there).
And, yes, a lot of stuff has been done to their AI. Unfortunately, we didn't test the historical starts where the Mongols are already present before releasing the current version.
They have their own CB-- not the regular Invasion CB. In fact, the problem is that their entire war AI is overridden by my code (and they can use no CBs except the ones my code initiates until it's "done" with them) but was written expecting their event troops to be marked in a certain way that they're not in SWMH in the later historical starts when already present on the map.