It looks like http://trilogymedical.net/welcome-member/ is protected by s2Member–i.e., it’s not a publicly accessible page. That page needs to be publicly accessible for someone to be redirected to after registering. The user is not logged-in automatically after registering.
It is possible to set up Auto-Login on Registration, but it requires a bit of custom code.
My suggestion is to set the success=""
attribute to a publicly accessible page that explains to the new user what they should do next (e.g., login). Then, you can use your “Welcome Member” page as the Login Welcome Page (s2Member → General Options → Login Welcome Page), which is the page users are redirected to right after logging in.
Regarding the Password Strength text and your screenshot: it looks to me like your theme is conflicting with the s2Member CSS styles and/or the JavaScript, which is preventing the password strength meter from working properly.
For a good idea what those forms should look like, see this example on the s2Member demo site.