I've got what I'm fairly certain are tubifex. They've been in my tanks since I started, they came in on some of the first plants I bought years ago. I've had them in tanks with kuhlis cories bettas and various others and the fish have never really done much to knock the numbers down -they only poke a little of their bodies above the substrate so they don''t really get eaten.
Personally I think they're neat (from a 'complex ecosystems are a good thing' perspective) but really annoying, I keep dirted/walstad tanks and they act like terrestrial earthworms, crawling around in the soil eating and then crapping it out at the surface, which is a huge PITA. It means that I have a constant source of super fine material on top of my sand cap -when I had cories in a tank with them the water was always murky brown as they stirred it up, and I have to clean the filter and prefilter constantly to keep it from clogging.
Right now they're only in a 10g shrimp tank and I've been putting off rescaping it for over a year at this point, because I want to kill them off before replacing the soil and replanting and I'm not positive of the best way to go about it.
As far as I know the shrimp don't eat the worms, unless one is damaged/dead on the surface. As for when to add them. Mine went in when I planted the first tank I did (so they went through the whole cycle) and they've managed to survive for years, including one point where there was nothing but shrimp in the tank and I didn't feed for months at a time, so they're pretty resilient. I'd say add whenever.