I have not had luck with the chemical route. While the chemicals won't harm the plants, I found that a) they didn't kill the caterpillars, and b) they did kill the bees that pollinate all my flowering trees and shrubs. To me, there is only one surefire way to rid yourself of tent caterpillars and that is burning - worked on witches, and works on caterpillars
I have numerous cherry and apple trees that caterpillars LOVE. Last year I purchased a really nice extendable pole trimmer. The Wolf brand ZM-V4 is extendable to 157" and has a simple and easy-to-use system for quickly changing attachments - loppers, saw, etc. I used this to lop off all branches that had nests. Once the nest crashed to the ground, I neatly trimmed it off and escorted it over to my backyard fire-pit. End of problem.
Sometimes nests are too high to reach, even with a pole trimmer. For those, I used an extension ladder to get myself up high enough to reach with the pole trimmer. Not everyone is comfortable on ladders, so if your nests are too high you may need to try the chemicals. (note that you'd still need to purchase a high-power sprayer that can reach those heights).
Either way, just make sure you get them when they're in their nests - early morning or late evening (basically dawn or dusk).
Also, remember that tent caterpillars don't fly or jump into your trees, they climb them same as you and I - right up the trunk. That's why many people put traps around the trunks of their flowering trees. This can be a simple fold of tin or even burlap - search the web and see how they're made. It's a simple concept that crawlers can't get past the fold.
Finally, you may want to keep your eye out for the eggs. They are fairly easy to spot. Again, search the web and you'll find lots of info about how to identify and remove the eggs.