yesss.... Your response, as well the previous one, gave the right direction.

The defined import function is *not* OK. Replacing it with something closer to what Exporter does seems to solve the problem:

package Demo2;

sub import {
    #${[caller]->[0].'::'}{$_} = ${__PACKAGE__."::"}{$_}
    *{[caller]->[0].'::'.$_} = \&{__PACKAGE__."::$_"}
        foreach grep { not /^(ISA|isa|BEGIN|import|Dumper)$/ } 
                      keys %{__PACKAGE__."::"};
}

use constant { 
    SUCCESS                          => 0,
};

1;
[download]

Now I just have to understand how come that it works :)