I have no idea if your vehicle will produce nuclear waste or not, I have never run one long enough to see it "run out" of one nuclear fuel rod. I've had one rod in my explorer for about 4 weeks now and I use it all the time and it still hasn't run out. And it's not "Weird" at all. If you separate any of the other fuel sources I showed you above and put only 1 (not a stack) in your vehicle and then move, those fuel sources would also "Disappear" and start to be used by the vehicle. This is normal behavior. And it's only radioactive when running if you add extra fuel rods to it's fuel slot. Extra fuel sources in the fuel slot are "Waiting" and will only be consumed by the vehicle when the first one of that item is exhausted completely.
You can see this same behaviour with any other fuel source in the game. If you put (1) coal in the explorer's fuel slot, then drive it, the coal will "Disappear" and the vehicle will drive on that (1) coal until the (MJ) of energy it contained is exhausted then it will stop moving. The same happens for nuclear fuel rods. If you some day use up all of the (MJ) of energy from (1) Nuclear Fuel Rod, the vehicle will stop moving. This is how the vehicles are currently coded in the game and this is all how they are supposed to work. Nuclear fuel rods are just another consumable fuel source like all other fuel sources in-game that the vehicles can use.