This plugin uses the function auth_attempt_script_login, which in the past was enough for getting access.
As of version 1.2.x this function offers less functionality than before.
This function is available in core\authentication_api.php
In order to overcome this, one needs to add 3 lines at the end of this function:

set the cookies

$p_perm_login=false;
auth_set_cookies( $t_user_id, $p_perm_login );
auth_set_tokens( $t_user_id );

Add these just before the comment line stating:

ok, we're good to login now (around line 279)

In addition, one can uncomment the line:

user_increment_login_count( $t_user_id );

It should look like:
user_increment_login_count( $t_user_id );
In that case still all logins are counted.

The change mentioned above can bring additional security risks in case you Mantis is on the WWW opposite an intranet.