Correct, with the exception of conversion from active skill gems, which applies first.
If you had a gem that does 50% lightning built in, alongside having 100% cold and 100% fire, your total damage would be 50 lightning, 25 fire, 25 cold. If the gem has 100% lightning innately, you'd do 100 lightning, 0 fire, 0 cold.
Conversion from skills has priority - this includes both skill and support gems. Otherwise this is correct.
The only distinction is between conversion from the skill vs conversion that's from the player/monster who's skill it is.