It wouldn't be black spot unless they were roses. You probably need to be watering more to help reduce the spider mites. Don't worry as much about getting the leaves wet because of fungal disease potential. The spider mites love hot and dry conditions and may do more damage than any leaf fungal disease you are likely to get there, plus they may help leaf streak get started. Using fungicides can cause other pest problems so it's better not to use them if you can avoid it and especially if you're using something that doesn't work for whatever problem you have anyway. That can also happen with insecticides, some cause an increase in spider mite populations for example.
