Black Mites on Rosemary

I live in tropical Singapore with year round summer weather of 32 degrees Celsius. I managed to cultivate 2 pots of rosemary since a year ago. Lately, I found black mites on the leaves and some of the new leaves have yellow spots too. I don't want to use any chemical insecticides because I need to consume the herb. Can you advise a safer non-toxic way to clear these pests?

Tape newspapers to the soil to prevent it from falling out of the pot and then swish the plant upside down in a tepid dishwash solution. Repeat twice at 8 hour intervals.