http://media.toro.com/CatalogDocuments/Product%20Literature/08-1012_tmc424e_ss.pdf My bad, not internet capable but absolutly has a zone delay. Great timer, despite the hate a lot of people seem to have for Toro. Why the hate?
I think the Toro TMC424 is capable of doing what you want.
Have you tried turning the controller off during a program? Does it shut the pump off? If it doesn't, try turning the power off to the timer. Once you turn the power off to the timer if it then shuts the pump off, it probably is a timer issue and not a relay issue. Im thinking that if the relay turns the pump on then its probably not the relay. I could be wrong on that but give it a try.
Look at your controller. If you have time programmed in for zones 9,10,11 etc. your pump will stay on. "Jump" wires from your last active zone through all remaining ports in timer to avoid this problem in the future. A small programming error can cause a lot of damage when dealing with a pump start relay.
I would say get a new one or just unhook it and try living without a rain sensor. If your a hands on person, you may find that you save a ton of money on your water bill by now relying on your sensor to turn your system off. This may sound wierd but I have found that people often overwater because they think that there sensor is doing the work for them. In most cases they are not. Sure it "should" turn the system off when raining, but its not intelligent, it doesn't know how long to keep it off ...
Is it a new sensor or a new controller. It may be wired wrong. Some controllers need "normally open" or "normally closed" sensors. ie; If your controller only accepts "normally open" sensors and you have it wired as "normally closed", that would shut the system off regardless of rain fall.
If your running off a pump and or preassure tank, I would start there.