As long as you are able to open mSecure on your devices, and the app is accepting your password, you should have no problems signing in to your account on msecure.com/login. The website account system on msecure.com simply signs you in to your account, which is the same account you are signed in to on your devices.
Real quick, when you open mSecure on your devices, what email address do you see at the top of both lock screens? Is it the same email address? Also, are you able to manually enter your password into both apps and is it accepted?