Currently hsl.fi does not offer SSO options in user login ('remember me'). Maybe this policy is chosen for security reasons.
Note that by default, separate web services have separate session management. User coming from hsl.fi must re-login in reittiopas, unless already logged in there. In this scenario, HSLID SSO would just make re-login more convenient.
It may be possible to use a shared cookie to implement a shared login state. Note that reittiopas login may not be valid for all hsl.fi operations (like purchasing tickets).