Is it newl or second hand? I ask because the alkalite fuel (motomix or aspen) don't have solvents in them, so if a previous owner ran it on petrol then you will have trouble starting it until the varnish has washed out of the carburettor. I know this from first hand experience of a £1k compressor that was factory tested using pump petrol and I only use aspen for my 2 and 4 stroke engines!
If that is the case (and worth trying anyway!), then empty the tank out and stick some petrol based 2 stroke mix in there and start it up, run it for a bit and then top up the tank with the motomix. My toy saw (ms180) was a sod to start and keep running for the first 5 or 6 hours of use and that helped until it got run it a little, so even new engines can be odd.
As to why the fuel is working it's way right through to the exhaust. I have no idea! Did you plumb the tank straight to the exhaust and by bass the whole engine or something?! I've never heard of that before, sorry can't help
All else fails, take it to a still service person and get them to look at it