You're right, spider mites are not insects but arachnids.
However, many/most insecticides work against mites because, while not identical they are very similar in many aspects.
In fact, many insecticides are formulated to be equally effective against both (check the label).
Imo, the only way to get rid of mites or insects during flowering is to vacuum them off. Time consuming yes but it leaves no residue of insecticide/dead mites to smoke.
Also, lower the temps of your growroom. Mites reproduce much slower at 70F than they do at for instance at temps around 80F.
It's essential to get rid of mites BEFORE flowering. The mites react to the cut in light the same way plants do. Cold weathers a-comin' so its time to make as many mites as possible to overwinter.
A few pregnant females around during the switch to 12/12 can totally ruin an entire crop.
P.S. the person who told you to use 3 different kinds of insecticides is spot on. You also have to use them every other day for at least 2 weeks, alternating with a spray of plain water on the off-days to prevent residue build-up.