The reason I didn’t give you the links is because I don’t want to be your first hand source of medical information. I can’t answer your follow up questions, I can’t clarify your confusions with the level of confidence I would like to, because I am not a doctor, not someone educated (beyond google) in topics involved here.

But my source of ‘alum preference’ is far from ‘a doctor told me so’. More like a doctor explained my experience - why after a shave (and aftershave) if I go out, for a brisk walk, or run, or hike - the sweat affects me differently based on my alum usage or lack of. If I don’t use alum, the sweat stings. Why alcohol doesn’t have similar effect. what is alum doing here, that alcohol isn’t doing. That question was answered by a doctor who happens to be a wetshaver himself. But he pointed me to enough documents that convinced the software/electrical engineer in me enough. But I still don’t want to be someone else’s first source of medical use of alum. That being said, here are some sources that mention the efficacy of alum as a vasoconstrictor or hemostatic agents.

https://www.scielo.br/j/ibju/a/33TK8r9RwFJLNv5GKpBGfHD/?lang=en

https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4163818/

https://www.researchgate.net/publication/265692280_A_review_on_common_chemical_hemostatic_agents_in_restorative_dentistry

https://magazine.zhermack.com/en/studio-en/astringent-haemostatic-vasoconstrictor-agents-impression-taking/