The chemicals actually disappear pretty fast in our hot, humid summers with heavy rain. What the plant has not already absorbed will be gone soon enough.
If you're going to put down fertilizer or soil amendments for your roses going into fall, I'd do that before putting down the new mulch though. You can't add enough compost and other amendments to our sandy soil! Alfalfa pellets (horse food) make a terrific soil amendment that also gives a boost of nitrogen. Roses love it, as do most other plants.