Custom Login page, redirection and restrictions

the redirect doesnt have a lot to do with browsers, have you try to clean firefox cache, it can be that.

also using ‘/distributors’ on users after succefully log in as url can sometimes not work, can redirect instead for the url link plus ‘/distributors’, is safer to use

home_url().'/distributors';

I use this function in functions.php to redirect on login

// redirects user after login
if (! function_exists('ctm_login')) {
    add_action('wp_login', 'ctm_login');
    function ctm_login(){wp_redirect(home_url());exit;}
}

so in your case should be something like

// redirects user after login
if (! function_exists('ctm_login')) {
    add_action('wp_login', 'ctm_login');
    function ctm_login(){
       $url = ( is_array( $user->roles ) && in_array( 'administrator', $user->roles ) ) ? admin_url() : home_url().'/distributors';
       wp_redirect($url);
       exit;
    }
}

this is the redirect after login, but one question, and if someone goes to the url and write “www.yourSite.com/distributors” will the page load?…