Soap may kill the ones on the leaves but they will still be in the soil. You don't want too much soap to be in your soil. Spinosad sucks, save it for killing mosquittos in a pool, pond, or birdbath. I gave it many chances and it did nothing against thrips, fungus gnats, or root aphids. Haven't had mites in ages so cant' say about them.
I prefer Doktor Doom foggers. Thrips are one of the easiest pests to get rid of. Also for in the soil drench next watering with a pyrethrins and neem mixture. They are both organic, natural, and break down quickly in light and oxygen. Pyrethrins is also the active ingrendient in the Doktor Doom. Do a spray with the neem/pyrethrins especially on the underside of the leaves every few days to get any hatchlings. Make sure you don't make it too powerful or it will burn your plant. You want to go hard though so they don't build up an immunity. Pyrethrins is extremely toxic to them and will kill them. It cannot hurt humans because we lack the receptors in our brain for it to hurt us. Neem slows pests down by messing with their hormones but it will not kill them. It is a good second line of defense because it will slow down any survivors. Then your subsequent pyrethrins attacks will really ensure death. It's best to try and get them in veg because it sucks having to spray anything on plants in flower. If you have to though just don't spray it 2 weeks before harvest so it breaks down. Don't use Pyrethrinoids. They are synthetic and take a long time to break down. They are stronger but more for non consumable plants. Keep Pyrethrins away from any pet fish. It might effect cats as well I can't remember I'd have to read the instructions again. It's very oily so you might want to wear gloves. I've had plenty spill on my skin and never had any ill effects though. I never wear a mask when I use it but try no to breathe it in. I notice sometimes it irritates my lungs when I use a lot and have trouble avoiding mist from the sprayer blowing all over.