Please make sure you have added the keys in Jomsocial > Registration > enable captcha option.
I just test on a fresh installation and its working fine.
If still, you have this issue, kindly share the admin login for staff?mods in private reply.
I will check it.
Your admin page redirected me to the Home page of site.
Please check and disable it so i can temp. have access for the site.
Something is weird. I can access the administrator backend in a conventional way, in other words, without the protection of Admin Tools. I also checked it out and all the extensions related to Admin Tools are disabled. Maybe it took some time or is a server thing.
Please, try again.