You are probably right. I dropped my Alum block intended for face use and it broke. So it is probably just a warning for the intended use.Looking at your picture, I believe that stick is one that is marketed for underarm use. If true, the quote is something quite common with underarm products. Supposedly, people suffer from dry skin there which would lead to cracking. I would image, since it is not meant to be rinsed off right away, getting alum into cracks in skin would be rather uncomfortable. I don't have any such warning on my alum block. If it is legal in France, EU, it should be safe for its intended purpose. They have been manufacturing and using it for a very long time.
As for use, I developed adult acne. If I don't wash daily, and carefully, I get breakouts. Chemical reactions aside, I don't wash my face daily. On those days, I apply alum. I have tested this by going without it for two weeks and did not like the outcome so I went back to using it 2 to 3 times weekly.