your conclusions are correct.
Just note that you'll HAVE to use fertilizers to get tiered fields. Without influence fertilizers all bars will go down by five, and one will go up by five. With 200% influence, all bars will go down by 5% and one will go up by 10%. Ideally, you'll want the right bar at 100% for tier 2 output, or the two right bars at 100% and 95% for tier3 output.
For tier 2, you'll get SOME tier 2 output as soon as the corresponding bar is over 50%, but it's generally not worth it. You might as well tier all the way up to a full influence bar.
edit: this a pretty old image, and missing corn, but it probably convenes the essentials more easily:
