If you decide to use the hose on your plant, be sure to devote some time to the underside of the foliage where mites are likely to congregate. You know that, already. And I like the use of a horticultural oil to help control spider mites. Let the leaves dry before spraying so that you don't dilute the oil any more than necessary. The oil will not burn new leaves. Again, it has to be applied to the underside.

The webs could be made by a regular spider...I have those little cobweb spiders that seem to stay busy all night long, but darned if I've ever seen the spiders. Or whatever it is that they're trying to catch!

The oil will only harm your leaves if the temperature is over about 80 F. I sometimes have this problem in my home rooftop nursery trees; like you I can't find them, but I discovered that if I wash them well with a hose end sprayer about 10 at night, they seem to go away.... and, as Rhizo said, pay attention to the underside of the leaves, where both spider mites and other teeny garden spiders hide. BTW late at night I can actually find the small spiders, but rarely the spider mites. Maybe it is my climate (warm and humid) that does not favor the mites; or maybe I just don't have them...I do have other types of mites, most important the one that carries citrus leprosis; luckily that one only attacks sweet orange; and I only have a cupla dozen of those.