Well, yes and no.
You do want to go to a reputable program, but you don’t want to split hairs, and you do want to understand which rankings you’re using. U.S. News simply sends a “peer assessment survey” to departments with doctoral degrees in a certain field, and they ask professors to rate doctoral programs in their area. It’s not necessarily about research output; it’s about professors’ perceptions of the quality of other PhDs in their field. That has some value (most professors are going to take research output into account at least indirectly) but also includes a lot of other unmeasurable aspects.
Nonetheless, reputation is kind of what you’re looking for when comparing programs. You should also think about the advisor that you’ll be working with - how productive they are, whether their research aligns with yours, what their reputation is like in the field, etc. Technically the University of Cincinnati is #3, but really Penn State or Florida State may end up being a better fit for you research-wise or advisor-wise.
So it’s a combination of “rankings” (not absolute numerical standards but general information about program reputation) plus your own assessment, and talking to professors in your field to see how they feel about how certain programs will help your career.