The reason to not apply certain lawn foods during certain times of the year has to do with how they work. Fertilizers, very soluble, quickly feed the plants growing there so if the plants are not growing, are stressed, lack adequate soil moisture, it is not a good idea to apply materials that force feed them but do nothing for the soil.
Compost, on the other hand, feeds the Soil Food Web which feeds the plants growing there. The nutrients in compost are not very soluble so they stay in the soil until the Soil Food Web makes them available to the plants. Compost then can be applied anytime, even when the turf grasses are stressed due to the heat and lack of soil moisture.

Thanks, Kimmsr. That's the answer I suspected and hoped to hear.
-Ryan

I agree. The application rate for compost is no more than 1/3 inch. That works out to be 1 cubic yard per 1,000 square feet. Put it out into piles around the yard and fling it from those piles. Then sweep it down into the turf with a push broom or drag a hose over the yard. Any grass blades which remain buried after you're 'finished' sweeping/dragging will suffocate under the compost. With zoysia the grass will not usually refill in the same season from suffocation, but it will refill next spring.