The label came off
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Oil creeps
A beard oil bottle is handled with oiled fingers by definition. Oil works under a label edge and lifts it, and a label that was fine in a box for six weeks fails in a bathroom in six days.
Alcohol is faster
A high alcohol aftershave that runs down the outside goes under the edge immediately and can attack the adhesive directly. The archetype warns about adhesives as well as plastics for exactly this reason.
The regulation does not care why
The ingredient declaration has to be likely to be read and understood under normal conditions of purchase, and a warning has to stay prominent and conspicuous. A label that has lifted or gone cloudy is a labeling problem, not just an appearance one.
Leaks at the neck
A dropper assembly and a fine mist sprayer both seal differently from a plain continuous thread cap. A closure chosen for how it dispenses still has to seal in a box on its side, and that is worth testing before a hundred of them ship.
Test the way the customer travels
On its side, warm, for a week. That is a weekend bag, and it is the condition under which a grooming product is most likely to be carried.
Where this shows up first
Reviews, not returns. A lifted label and a slightly sticky bottle rarely come back; they turn into a complaint about quality that never names the adhesive.
What to ask the label supplier
Name the contents, not the container. "A 30 mL amber glass bottle" tells them nothing useful; "a high alcohol aftershave that will run down the outside" tells them which adhesive and which face stock to quote. They know the answer and they cannot give it to a question about glass.
And the tin is its own problem
A curved steel wall with a lid that slips over it leaves very little flat area and a seam the label has to cross or stop short of. A label that crosses the lid line seals the tin shut the first time it is opened, which is a design decision rather than an accident and is worth making deliberately.