Scheduled Jobs page doesn't handle multi-site correctly

When using multi-site, the two (or more) websites share a single settings page for "Scheduled Jobs". (civicrm/admin/job?reset=1)

And yet separate consolidated cron tasks were needed to send out mailings from the different sites, despite the shared scheduled jobs and sent mailings pages. This is very confusing and inconsistent - the "Scheduled jobs" page for my second site was informing me that mailings were sent out ten minutes ago, yet that job only sent mailings for the first site.

It would be good for parts of CiviCRM affected by multi-site to be clarified in general, perhaps a visual indication on the administrator pages if the settings page is for the current site only. At the moment it is vague which bits of CiviCRM are affected by multi-site or not.