Ever seen a Harley Davidson Golf Cart?
Silly thing was a two cylinder, two stroke engine
with two sets of points, starter would spin backwards and it would fire off the other set of points and run backwards whenever you needed reverse.
Although rare but almost any engine
can be made to run backwards, but usually very badly cause the timing is way off.
Nothing else I can think of would account for your symptoms, I would check my fuel
injection timing though, I'd be surprised if it wasn't too advanced