Nothing is bullet-proof. However, I spray cuts and seedlings with 1-1/2 cup 3% hydrogen peroxide and 1 tsp ag soap in a gallon of water. That kills mites and mite eggs. It kills PM and other fungus, and most species of insects and their eggs. It also kills a lot of other micro critters. Use enough to drench the soil. The roots like the H2O2 oxygen given off. I use this spray and quarantine any new cuts or clones, no matter the source or what the grower tells me. I assume that all new plants have mites, ants, aphids, scale, whitefly, PM, phylloxera and soil gnats. This spray is pretty cheap, and non-toxic for the most part. As long as you do not drink the stuff, you should be OK.
If you want to go full nuclear, you can add Avid (abamectin) to the formula but that is toxic and you need a spray suit and respirator and goggles when spraying that stuff. But it works. It is the only spray certified by the USDA to kill 100% of broad mites. You always need to use an activator with Avid, and the ag soap works as that. Avid will beak down in about 6 weeks to undetectable levels. Spray it at night, as Avid is photo-degraded. A far less toxic upgrade spray and drench additive is refined Neem Oil. But you want to spray refined neem oil when it is 78 degrees or less at nightfall or lights out, or the oil can burn the leaves. You do not need a suit or respirator with Neem oil. Also you do not need an activator (ag soap spreader) with refined neem oil. Raw neem oil is different, and very hard to dissolve in water and work with as a spray. It works well as a drench though.