Frostferno - Combat Focus - Conversion

Hi there,

even after a lot of google search and POB tests, I do not really understand how frostferno works with ele hit and combat focus.

frostferno gives cold to fire lvl 30. that means i would want to have my elemental hit with cold damage.
but if i change it in POB via combat focusses to fire damage, the damage almost doubles. It makes no sense, if ele hit deals fire damage. cold to fire gem cannot convert anything, nor add the %of cold as extra fire damage....

it gets even more crazy when you add avatar of fire to that. Which is a weird mechanic as well in that combo. because it converts a possible form of damage before combat focus kicks in , right? but thats totally random. Is POB here incorrect? because with avatar of fire the damage almost doubles again...

can anyone clarify for me the conversion order here and why that phenomenon is happening?