Damage meter addons log info from the combat log. So if the addon is wrong then the combat log is wrong. Which is unlikely that it is. There’s no way to know for certain unless someone tests it.
The only way to properly test it is to get a 2.8 speed MH and a 1.3 speed OH and go do 10,000 melee swings and see if HoJ melee has variable hits to indicate that a MH proc occured. Otherwise it’s safe to assume that it only procs OH melee swings on melee HoJ procs.
Both the 2% proc rate and abilities procing MH work normally in the testing i did.