It isn't just that the nodelet is cached. Even if you got a brand spanking new rendition of the Other Users nodelet contents, it would still show you as "logged in" if you had just recently "logged out". The caching of the nodelet content is required to explain why you might not be listed immediately after you log in, though.
It wouldn't make much sense for the act of "logging out" to be what removes a user from "Other Users" (for one, logging out from one browser doesn't say anything about how many other browsers I'm still logged in via). Certainly, a great many users of this site almost never "log in" (enter their password) nor "log out". Users visit PerlMonks either anonymously or as a particular user. Visiting as a particular user (without having flagged your usage as "for ticker access", that is, presumably non-interactive use or alternately "cloaked" use for whatever reason) counts as "having been logged in recently" (short for "having visited recently while logged in").
What Other Users shows is simply users who have visited recently (obviously, not anonymously). After you log out, you have still visited recently (you have to visit in order to click the "log out" link, I think).
There are technical problems with having Other Users be up-to-date every time it is displayed with up-to-date information about relative idleness. Last time I looked at this, a long, long time ago, I was worried about the cost of adding an index to a fairly large table on a field that would be constantly being updated. And I've certainly seen bottlenecks related to this feature. But thinking about it now, I believe an index would be a net win despite the constant updates, even if we don't start re-rendering Other Users frequently.
But I still don't want an "idle" time shown in the nodelet. I think that would put too much emphasis on visitor's habits and in too much detail. The nodelet already communicates "idle time" by answering "have they been idle for more than a few minutes?". If you want more information on idle time, visit the monk's homenode. But note that even that information is not very accurate if the monk has visited recently, as that information is pulled from the node cache and we don't want to invalidate the cached copy of your user object every single time you load a page.
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