Front derailleur twist shifter replacement - from small to big ring in one click
My first thought is that the new shifter isn't compatible with the chainring spacing, but unless this group has a super-narrow profile I can't think of one that would be as wide as a typical first-to-third chainring spacing.
In my experience, the markings on twist-type shifters are not always equidistant, and may be due to non-linear throw of the derailleur or non-linear take-up of cable in the shifter. Check that the cable is properly routed through the shifter as well as to the derailleur pinch bolt. I have seen the latter cause this issue.
If you have an alternate derailleur (top swing vs. bottom swing) you can try that if space allows.