Also, the reason I ask about it turning off is that some come on when it only passes a certain temp, but do not shut off it the high fan is about to kick on. If I have two of them running I do not see why I would want power going to both the high and low at the same time, it should be one or the other.
Most setups running the 2spd fan run like this and it works ok. I tested mine and found that running power to both high and low did make the fan run a little slower than running just high speed. I'm sure it doesn't help the amp draw either since the high is basically being dragged slower by the low, but I never tested amp draw to be sure.
I was able to resolve this by adding a SPDT relay in front of the low speed switch power. This relay is ON until power is applied to the switch terminal, so when my controller turns on High speed, this applies switch power to the SPDT relay and turns off the switch power for the low speed relay.
I have set up a completely reliable controller/relay combo to run my fans and it has been working great for many years. For the fan relays I have 2 HD relays I bought from a robotics website that are rated for 150amps cont. (I think something like $20 each but it was 10 years ago), a Haden 2spd fan controller, and the SPDT relay. It works great, is adjustable, and the only failure I've had was a cheap parts store fan controller I ran for about 8 years before I installed the 2spd controller.
That said, I'm in the process of swapping to a Volvo fan and controller since I had to pull my radiator for an unrelated project (I've had the parts for months). There is nothing wrong with what I've been running, but the Volvo controller is clean and simple. I'm going to pick up a couple extra relay packs from the junk yard as spares just in case. Since this setup is new to me I can't comment on the reliability so I want to have extras to be safe.
If you have questions about the Volvo controller, there is another thread with tons of info specific to that.
Just for kicks, here is everything I have been using to run my fan. Again, it has been 100% reliable, and if there was a failure it's simple to bypass and run manually, but it's complex to say the least.