Entering a hashable cron value like @midnight, @daily, or H 4 * * * in the "Poll SCM" field of a job seems to ignore the hashable part, and the value 0 is used instead.

i.e. Jobs scheduled to poll @midnight actually do occur at midnight (according to the text in the config page; see screenshot), and polling scheduled as H 4 * * * is shown to always start at minute zero of that hour. I would expect these to happen — as documented, and as works for "Build periodically" — at pseudo-randomly chosen times.

I've seen this across various different jobs, so it wasn't just luck that I happened to see 12:00 come up as the "midnight" time.