so here are a couple things about neem oil... i use it and swear by it so ill give you my personal experiences with it...
first i've used neem oil under HO satellite IV floros on a 24/0 crop with NO problems.. i didnt have any burn from the water or the oil magnifying light... no ill side affects at all.. so if you are using floros i would venture to say you'll be fine spraying during a 24/0 light schedule... just move the lights when you spray so you dont spray the lights themselves... make sure you get under the leaves and the "inside" of the plant just as well as the topside of the leafs and "outside" of the plant... like was said those little bastards live under the leaves so take time to spray well...
secondly neem oil can be root fed to your plants as well.. during the entire time i have an infestation i feed neem to my plants... ill explain what neem oil does and why root feeding is good in the next paragraph.. but i feed each plant about 6 ml per gallon of water every other feed.. you can just incorporate the neem into your regular feeding schedule... only do this if its soil though... i wouldnt recommend it for hydro...
here is how neem oil works.. neem oil is NOT a spot killer.. you wont spray your plants today and be gone of mite tomorrow... expect about a 2 week battle... neem oil works a couple ways.. first if you can spray the eggs well it covers them and suffocates them... no more eggs.. when the adults eat the neem oil it messes with their hormones... it makes it so they cant reproduce and lay eggs.. immature pests that eat the neem oil dont reach adult hood and are never able to reproduce... thats why spraying the plant well is so important.. you want to make sure the mites have no choice BUT to eat the neem oil... root feeding work very similar in that the pests hormones get fucked up when they suck the juices from your plant, but it also deters them from sucking on your plant because the neem oil tastes horrible... it also contains some trace minerals so its actually good to feed your plants,, i personally will root feed my plants every other time during and infestation, and spray them every 2-3 days.. the spray i use is 3ml neem oil per 1L of water with a few drops of biodegradable liquid dish soap... usually following this over a 2 week period.. then just go down to spraying once a week as a precaution... ill do this up to the 4th weeks of flowering.. havent ran into mold problems yet, or had neem flavored buds, or any other side affects due to the neem oil... its always worked for me.. like i said.. it just takes about a week before you see progress, 2 weeks before the infestation is gone... but its a natural way to get rid of them... if you want an immediate solution get some NO PEST STRIPS from walmart, lowes, home depot, ect.. they will work in a few hours and kill both mites and eggs... but it is a chemical strip (not a spray)... personally i dont want to think that what im inhaling was treated with a chemical... NO PEST strips work tho.. just make sure you arent in the area because they arent anything you want to breath in... also AVID and FLORAMITE are instant working sprays, but again they are chemical... chemical = instant, but it is a chemical you are using on your plant... natural = longer time fighting the pests, but its not chemical.. just depends on you...
also.. a couple smaller ways of helping slow down their life cycle and battle them is;
1) keep humidity up... they hate humidity... spraying with cold water will help by raising the humidity, spraying them off the leaf surface, and they dont like cold.. which brings me to number two..
2) drop the temps to between 65 and 70 if you can... it can take 10 days for mites to reach maturity in cooler humid temps, but as little at 2 days in warmer less humid places... each female can lay 100 eggs a day... they are 75% females anyways... in the right climate they can very very very quickly run your garden over... so until you decide how you are gonna deal with them and they are dealt with making the enviroment as unhospitible to them as you can will help slow their growth...
3) also you can use a tobacco, tobasco, garlic, cinnamon oil, peppermint oil, ect spray.. they arent pesticides, but will help deter them from your plants...
whatever way you chose is up to you... some say neem oil doesnt work and you should go with avid, floramite, or no pest strips... i swear by neem oil and wont use anything else... just make sure you get 100% neem oil from the first press... and not 100% neem oil from the second press or something that just has neem oil in it...
good luck with those bastards.. hope this helped