OK that is clearer.

Is that documented anywhere? I don't recall having read it before.

Thanks for your help!
This post is thus not a bug, and can be closed.

Step 5 specified precisely that joining the game while appearing in the admins list (and with the configuration file loaded beforehand of course) does not promote the said player to admin, as it is expected.

Here is the scenario:
Joined a game hosted by a friend on his PC (v0.15.10)
Saved the game to mine when he left (server closed)
Uploaded the savegame to a headless server (v0.15.12)
Configured the server-settings.json file with a directive as following:
{
[...]
"admins": ["foo"]
}
Joining ...