A couple of reasons this might be happening. The exhaust gasses do contain water vapor, and if they cool down to the point where that water vapor condenses on the inside of the pipe because the pipe is not warm
enough then you will get water collecting. It makes sense that it is at the end of the pipe where the gasses are coolest, and the cold outside air is sucking heat out of that end of the pipe. The chances are hat tis pipe is slanted slightly up, and so the water will flow back into the pipe, collect around the cleanout, and leak out through the seal.
You may notice this effect on a motor vehicle where you see water coming out of the tailpipe when the engine is cold, but not when the engine is hot. This is because the exhaust pipe has warmed up and so the water escapes in gaseous form.
Another possibility is that the internal diameter of the exhaust is big in relation to the volume of gasses flowing out. When this happens, the gasses swirl around inside the pipe instead of flowing smoothly in one direction. It may even suck in cold air from the outside and mix with the exhaust gasses in that last section. This mixing will also cause condensation to form. Maybe try restricting the exit hole and see what happens. It will create a back pressure so best to do this once the fire is drawing properly otherwise you might fill the room with smoke. But this back pressure will cause the exhaust gasses to flow more uniformly and eliminate any back draught. It might be an easy fix.
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