Hi Janardhan,
There are a few things that could be the issue. One possibility is that your 2 facebook profiles were connected together instead of logging into a second facebook profile.
If that is the case, you need to make sure you are using the authentication flow documented on
https://singly.com/docs/authorization, specifically the logic of whether to apply an access token to /oauth/authenticate.
Once that is fixed (it should be correct if you use our library). You will need to create a new Singly app and use that in order to reset the connection of the accounts.
I'd be happy to answer any other questions.
Justin