The first 3 levels get you conditions improvement.
The next 3 levels get you value improvement
The next 3 levels after that get you atmosphere converters.
I can confirm that it is wrong. Test game, finished atmosphere converter on gas giant inhabited by none breathers on turn 2401.2. On 2404.2, ten turns after the atmosphere conversion should have taken place if it were possible, the planet was still gas/methane.