Description is wrong indeed. What leveling up monkey king actually does, is reducing cooldowns:

lvl 1 (base): 4round cd, 2round battlefield cd (usable on 3rd round with 4 round cd= r3, r7)

lvl2: 3round cd, 2round battlefield cd (usable on r3 with 3 round cd = r3, r6, r9)

lvl3: 3round cd, 1round battlefield cd (usable on 2nd round with 3rounds cd= r2, r5, r8)