Tempo SC Ultra is not labeled for Spider Mites. For spider mite control, consider Bayer Advanced 3-in-1 Insect Disease & Mite Control.
We do not carry and therefore cannot comment on Tempo SC Ultra Premise. We do, however, carry Tempo SC Ultra and can tell you that the product is labeled for a large number of insects and is safe to spray indoors along baseboards, cracks and crevices. Kids, pets and everyone else needs to exit the area to be treated at the time of treatment and can return once the treated area is completely dry. Approximate drying time is about 2 hours.
Tempo SC Ultra is labeled only to use as a crack and crevice spray around the perimeter of the room. It is not labeled to be used on mattresses, furniture or other items that will be coming in prolonged skin contact. You can use Tempo SC Ultra on your box-spring. We have linked the Tempo SC Ultra product label in this answer so you can review the label for complete usage instructions. We recommend using Bedlam Plus for spraying your mattress.
Please take a look at our How to Treat for Bed Bugs Article for step by step insructions on how to do a full treatment.
Tempo SC will not actually repel mosquitoes, but using it in target areas will help reduce the number of mosquitoes in your yard. Tempo SC Ultra should be sprayed on the underside of leaves on trees and bushes to help control mosquitoes. Mosquitoes like to hide on the underside of leaves during the heat of the day so spraying there will help the mosquitoes come into contact with the Tempo SC.
You should start spraying before the egg hatch. To find the correct timing in your region you should contact your local cooperative extension office as the timing varies from region to region. Cooperative extension locator: http://npic.orst.edu/pest/countyext.htm