There really isn't a whole lot of hazmat education beyond perhaps aweness that an EMS provider really needs to know.
Firefighters need more.
An EMS responder (even as part of an FD) should never be in a hot zone, nor in a warm zone, and absolutely not involved in decon. Let the people who are supposed to handle that do it.
What EMS really needs to know is to not accept any patient who is not properly deconed no matter what is wrong with them. It is a risk that makes patient care unsafe. Even if you are dressed in a gumby suit and SCBA, nobody at the hospital is.
Also not taught in class, remove any unrequired stuff from your truck. Make sure your driver is not involved in pt care. Duct tape your internal compartments. Remove the matress from the cot. Drape the pt compartment in garbage bags and any equipment that is not really expensive, should all be in the drape and thrown out when you are done. Ask the hospital for some scrubs and ditch your uniform too. (If you ever have to decon every surface of your truck, you will remember this advice.)
The above will limit the possibility of any accidental exposure from patients who do not get appropriately deconed for whatever the reason. (Field ops are seldom perfect, and unless you handle hazmat regularly enough to make it look like art, mistakes will be made.)
Almost forgot, the unit that is monitoring responder health should not be in anyway inolved with transporting patients.