If you are using the Login API (/api/login) - this does not create an SSO session.
The FusionAuth Login pages do not currently use the access_token or refresh_token cookies for session management.
If you want the SSO feature - you need to use the FusionAuth login pages. This is the strategy outlined in the 5 minute setup guide: https://fusionauth.io/docs/v1/tech/5-minute-setup-guide
We do have a feature open to switch to token based SSO so that this use case would work: https://github.com/FusionAuth/fusionauth-issues/issues/358