These (if they are really tiny, and leave a bit of red dye when smashed) are
actually common red spider mites. A miticide can kill them, but only if you
can see a plant where they have attacked in force. The attack looks like
little white spots because the spider mites have special mouths designed for
sucking out the centers of plant cells.
Garden centers usually don't use miticides though, they typically use a
specialize lady bug which usually feeds on aphids or mites, or sometimes
they'll bring in another kind of mite called a "predatory mite". Not
recommended for the inside of your house though.
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