Dear Xavier,
I made a virgin Joomla! 3.5.0 install on my local WAMP server with PHP 5.6.25 and also installed plug-in Login One! Business Edition for J3, version 2.3.2.
I registered a new user with log-in username roberto and displayed name Roberto D'Allura. Joomla would not accept a username containing an apostrophe, but only in the displayed name.
I found that the plug-in performed without mistake. It blocked a second concurrent log-in by roberto and displayed the message that he had to wait X minutes.
In other words: I cannot reproduce the problem.
So my question now is: what exactly is your plug-in install doing wrong? Where is your apostrophe, in the username or the displayed name? Do you get an error? If so, which one?
To be continued...
I will still email you about the other matter. Regards, Rob
PS: The download link had expired because there have been plug-in updates since your order. The update process follows a different path, as mentioned in my previous note