With M-x jabber-get-time, you can ask what time an entity (client, server or component) thinks it is, and what time zone it thinks it is in.
You can query a server about when a certain user was last seen online. Use M-x jabber-get-last-online for that.
You can also ask a client about how long a user has been idle with M-x jabber-get-idle-time. Not all clients support this, e.g. jabber.el doesn't. This command can also tell the uptime of a server or component.