SSR doesn't actually need 12V right ? I see most of them at 3-32VDC ( actually 12V is for the electromechanical relay )
Yes the SSR input is 3-32V DC, but the controllers with a relay "output" are just that, a relay with NO, NC, and COM terminals (the relay is internal, it's not an output to drive an external relay's coil). You would then need your own 3-32V DC source to connect to the relay terminals to control the SSR.
IandB: A PID controller is just an control feedback loop using proportional, integral and derivative values. It doesn't have to be super fast to be a valid PID controller. If you are monitoring the temperature at one point, and the cooling/heating source is far away, and it takes 5-10mins for the temperature to change, you could easily overshoot it with just an On/Off thermostat.
The PID controller needs to be matched to the environment its controlling. If you are controlling something like a DC motor then of course you need something fast.
Doing tests previously with my mini oven, if I turned off the element once I reached my target temperature, it would continue rising to 40-50 degrees over!
On these you can set the control period from 0.5s all the way to 2mins. It only samples the temperature a couple of times per second anyway.
When its running, you can change the bottom display from the set value to an output value. It shows something like A 100, A 63, A 0 etc. I'm guessing this is the "analogue" PID output value from 0 to 100%, which is then used with the control period to determine the output on time. ie A 50 is 50%, so with a 4 second control period it would turn on the output for 2 seconds, and then off for 2 seconds.