How did they grow so fast? The largest a kingdom ought to be after 13 months is only 16 hexes, assuming that for the first ten months you claim the maximum of one hex each month, and then the last three months claim a maximum of two hexes each month.
From my own experience (my group's kingdom is 6 months old), I think you would run out of money to keep up with the Control DC. 23 hexes + 2 districts (I'm assuming they haven't added any districts to either town) is a DC of 45 for kingdom checks. My group's kingdom has stopped adding hexes for the time being because their Stability and Loyalty checks were getting difficult (Economy is not quite automatic, thanks to Unrest), and they started with more than the standard 50 BP.
It is certainly possible, using the Ultimate Campaign rules, to build a kingdom that adds a new hex every month from the first month until you run out of hexes to claim... but that assumes two things: that you allow farms to share hexes with mines/quarries as per the asterisk, and that you don't get any really bad random events.
For example (assumes that kingdom leaders have an average of +3 bonus in their prime stat):
Month 1 - Claim the hex with the Stag Lord's Fort, build a Farm and Quarry, prepare a site for settlement. (cost: 13 BP, taxes ~9 BP, treasury 46 BP)
Month 2 - Claim the river hex to the northeast, build a Farm and Quarry, begin settlement and build a Castle at reduced price. (cost: 38 BP, taxes ~12 BP, treasury 20 BP)
Month 3 - Claim the hex containing the Sootscale Caverns, build a Farm and Mine, build a Mill in the settlement. (cost: 17 BP, taxes ~15 BP, treasury 18 BP)
Month 4 - Claim the hex containing the Rickety Bridge, build a Farm and Quarry, build a Library in the Settlement. (cost: 17 BP, taxes ~17 BP, treasury 18 BP)
(Notice that, at this point, the kingdom is now breaking even on spending vs taxes when they roll average for their economy check, and have no Consumption.)