Pest free garden

Howdy, I love gardening and I have a beautiful chrysanthemum garden. Recently, I saw some black and red spots on the leaves. Some of the leaves turned yellow too. I guess the soil drainage could be one reason behind it. I couldn’t identify the real reason of the colored dots. My friend who visited my garden said that the dots might be due to spider mites. While searching for a solution, I saw a blog in which they have mentioned some ways to avoid pests. [ http://inthebackyard.ca/how-to-have-a-pest-free-garden/ ]. It says that using a mixture of dish soap, cooking oil and water is a good spray for spider mites. I haven’t tried this before, and I need some suggestions. Is this mix helpful for avoiding the mites? Should I try chemical pesticides for faster results? Please help me out with suggestions.