nevadawalrus was typing at same time as when I replied!
When a HM100 is hunting and surging that fast the backfireing is normal!
Try choking the carb little bit at a time to see if it ever settles down any if it's still surging after it's run for longer than couple minuites. (cold surging is normal at start-up) The cold engine surging when a Tecumseh HM100 with a Al Gore carb on a gen is another one of the reasons that Tecumsehs get cursed and people lose their religion easily.
That's a symptom of a restricted carb, but you say the carb replacement is NEW!
I would look for a air leak on both side of the intake manifold since you have a NEW carb.. Might try squirting some oil around the intake at the engine and at the carb to mainfold base. If it's leaking it will momentarily smoke and make a different sound when it sucks the 30W oil!
It that is a used carb the jets are restricted due to trash. Even the low speed jet being restricted will cause that on a Al Gore non- adjustable type carb. (try holding the carb linkage governor at idle and see if the engine idles ok!) If it idles ok the high speed jet is restricted or fuel delivery issue. If no low speed idle, back to the air leak, low seed idle jet area.
If it has the high speed adj jet carb, try adjusting the needle on the bottom of the bowl! It's a Air/Fuel delivery issue most likely! Just be aware that the HM100 has the following symptoms with the low emissions type carbs:
When you get it going running right the engine if it's a non adjustable carb the HM100 will sound EXACTLY like that for about 20 seconds or until the engine warms up (and sometimes for 30 seconds when weather is 32 degree or below) then run ok AND the non adj jet carb HM100's will sound exactly like that for couple minuites when running out of fuel from the tank or running the carb dry of fuel.
A adjustable high speed jet carb for a HM100 (which are hard to find and cost about $100) can be adjuted so as the engine just dies when running out of fuel, and also no hunting and surging during warm-up!