The REST API session key is not the same as the web ui session, so logging it out will invalidate the REST API session, but will not affect the web ui session, so if you are signed in via the web ui, you will still appear online. Authenticating or logging out via REST V1 should have no effect on your online status.
To sign out of the web ui, you can hit the signout URL in the community.
If you are using Lithium SSO, we also provide a way to sign a user out using an SSO token that sets a special SSO id ($LiAnonPlz$) that represents the anonymous user (in the java SSO client, use the LithiumSSOClient.ANONYMOUS_UNIQUE_ID field, for .Net use the SSOClient.ANONYMOUS_UNIQUE_ID field, for PHP use the $lithiumSSOClient->ANONYMOUS_UNIQUE_ID field). See the SSO Client guide (attached to the page and called something like LithiumSSO_Guide_15_12.pdf -- version may have changed from this) for a code example.
-Doug
