While I agree with what Don suggested, that is logical. I usually put my meat in about 200, minion start very similar to what you described, and I have never had an issue controlling my temps with the dampers like you described!.
First of all, make sure the thermometer you are using is reasonably accurate. My original Equipment Thermo on my WSM cannot be relied upon! it reads way too high, and is erratic, which initially led me to believe my cooker was running too hot, when it was not!
If you are happy with the intigrity, and accuracy of whatever thermo you are using, I would then be looking for air leaks on your cooker, if you have all your bottom dampers closed, and your temp is still climbing like that!, you are getting un-wanted air in there, to "fuel the fire", from somewhere else.
My cooker is tight, meaning when I am done cooking, I can close all dampers, top & bottom, and the cooker is cold whithin 1.5-2 hours!.. sometimes faster!
If your cooker won't shut down like that, that confirms that you have a pretty good air leak somewhere.
If you have one of the new 22.5" WSM's the original door has been notorious for a poor fit, and that can allow a lot of air in. My original door did not fit very well, and even though I could still control my temps adaquately with it, I bought the Cajun Bandit stainless door for it, and it has been way better at creating a tight cooker than the original door. (looks better too)
I have read that some people have received cookers that have a warped, or out of round bowl, lid, and or cooking section. This will also introduce un-wanted air into an otherwise temp controllable cooking environment.
Ther are a number of possibilities here, and I am sure you will receive other opinions as well as mine. What I state above is just my opinion, based on my own experiences.
Another thing that has helped me to thouroughly understand, and control my temps, is to NOT think of the charcoal, or lump, as my fuel. I think of the charcoal as only a catalyst !, and Oxygen as the fuel!... if you can adaquately control the oxygen intake, you will control your temps!