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Lots of conversations about pubs coming out of grad school. Let me bump up a few years to conversations at 3rd-year review and tenure. Only 1st author pubs are really discussed-since they are seen as defining your research agenda, they are read and reviewed by committee 1/n
At both 3rd-year and tenure review, # of pubs are counted that are not with previous mentors. It is expected by 3rd year that you are forming an independent research program that does not involve pubs with former mentors
Pubs where you are 1st author but has a long list of other authors are often targeted with lots of questions because the individual contribution is questioned. If senior professors are on paper--even more questioning of indiv. contribution
Until you are a senior professor or in a more bio-oriented area of psych, senior authorship are not really counted. Though if other authors are students--then you get "head of lab" credit and publishing with students (this is strongly considered at 3rd year and tenure review)
Publishing research from your dissertation doesn't hold as much weight as it use to, but is still often mentioned if published in a "major" outlet. Single author also doesn't hold the weight it use to--but can be positive if you have lots of co-authored papers
h-index is often mentioned but due to questions about it's validity, it is generally an off-handed mention. Instead trajectory of pubs and citations are discussed and generally the criteria used for productivity. We often use bar charts to show upward projection of productivity
Each case has its own story, but each of these topics I mentioned are discussed at all cases I've been involved with, in the last 24 years. Hiring is less clear and more idiosyncratic and # of pubs are sometimes discussed but quality and fit of research are usually the convo.
Disclaimer: my entire career has been at the University of Michigan--so this is my only experience. Other departments and schools may vary on the emphasis even though my writing of external letters for other universities generally ask the same questions
