Let me answer from the perspective of a liberal arts college that emphasizes both teaching and research. I'm going to tell you how I've seen research assessed. I don't claim that this is a good way to do it, but hopefully the transparency helps. I wish someone had written an answer like this before I went up for tenure, because I would have found this kind of inside-information very helpful, and knowing more about the process would have taken away some of my stress. Hopefully this answer serves that purpose for some future reader(s).
I've been on more than 10 hiring committees. We never used any of the journal rankings. We assessed research strength based on the number of publications, general knowledge of journal strength (e.g., the Journal of Topology is better than the made-up Mid-Atlantic Math Journal), number of preprints, research statement, and letters of recommendation. What matters most is some demonstrated capability to succeed and finish projects, a well-articulated research trajectory, explaining it well in the 20 minute interview, and the job talk if they reach the on-campus phase. We want to know that the candidate is a "self-starter", who can maintain their research program even if there is no one they will co-author with in the department, and that they have a trajectory to amass enough research to be successful at tenure.
I've also been on several committees that assess candidates at the time of tenure and full professor. In these settings, journal ranking lists could play a role, if the candidate's research is borderline. For example, at tenure time, if a candidate has more than six papers in good journals (where "good" is again assessed by general knowledge of journal landscape) then they are above the bar for research. But, if they have 3-4 papers, then members of the committee might feel they need to really check if those journals are good, and it can be the case that no one on the committee works in the specific subfield of the person under review. I've witnessed people referring to the Australian rankings in these discussions. Furthermore, external letters that assess the candidate's research do sometimes refer to these journal rankings. In my experience, the most common one that gets referred to is the Australian one:
https://www.austms.org.au/Rankings/AustMS_final_ranked.html
https://www-users.cse.umn.edu/~arnold/math-journal-ratings/
There's also a Chilean one, where journals get marked as either MB (muy bueno), B (bueno), or R (regular). And I know from a co-author in Chile that this does matter for hiring, promotion, and grants.
There are also rankings from Norway and Finland but they include all journals in the sciences, and math journals are essentially always the bottom because we have a lower impact factor, because of how citations work. Impact factor can also be used, and whether or not a work has been highly cited.
Assessing someone's research is hard. Fortunately, when our professors go for tenure or full, they submit a written statement that again explains their research and their research program, and that helps a lot. The external letters also help a lot. Journal rankings and impact factor play a miniscule role and I don't think anyone would ever fail based solely on them, because that would be asking for a lawsuit, because of the signal-to-noise ratio in any assessment of journal quality. From the candidate's point of view, to avoid this source of uncertainty, it's best to be safe and not be in a borderline research situation.