JD, this is a common problem and will only get worse! Well, it need not get worse once you get a handle on how to control things. There are definitely key factors involved which have been mentioned, like type of wood and amount of moisture in the wood, etc.
You might like to know that we also had that problem when we started with the Fireview.....and at the time I really got no good advice on how best to stop problem; therefore, we experimented.
This time of the year we rarely put in more than 4 small splits and more usual it is 3 splits. We don't load this baby up until it gets cold outside! Then when it gets cold, you have to keep an eye on the coals or you will only be able to put in the 3 or 4 splits because there is no more room! Also, you can't empty ashes.
The simplest way we have found, and I'll use cold winter time burning for example, is to watch the stovetop. When the temperature is down to 500 or even 550, start opening the draft some. If 500 then I'll usually go right to 2 on the draft control. When the wood is almost all burned but you can still see where the log was, that is, it hasn't yet busted into nothing but coals, turn that draft on full.
At that point do not worry about heat going up the chimney. You just want those coals to burn down as fast as you can get them to burn down.
After maybe a half hour on full draft it might pay to rake the coals towards the front of the stove. At the same time, rake through all the coals to loosen them up which allows more air circulation for burning those hot little buggers. We will sometimes do this twice if we have lots of coals.
Then again, when reloading, rake the coals to the front of the stove....always. Place your biggest piece of wood in the bottom rear of the stove. If possible, put a faster burning piece in the front bottom, then finish loading however you want. This gets the new load burning quickly but also allows for a longer burn.
Good luck and I hope I haven't made this confusing as it really is simple.