A page cache serves the copy it made, so a page cached inside the window can still show the wheel after it ends, and one cached before the window opens can show no wheel once it has. The plugin empties the page caches it knows (the same list as for an update, below) when the window opens and when it closes, if the wheel is on. That happens on the first visit that reaches WordPress after the moment, and not for the days of the week or the time of day. A new time zone under Settings → General moves both moments with it, and if the wheel is on and the change opens or closes the window there and then, the caches are emptied once. A host's own cache, or one not on the list, keeps its copy until it expires: keep the pages this appears on out of your cache if the timing has to be exact. A spin is checked against the schedule when it happens, so a wheel on a cached page cannot hand out a coupon outside the window.
Nothing about the schedule itself is approximate — it is worked out against your site's own clock, under Settings → General.
Still stuck? Ask the developers who wrote it. We aim to reply within one business day.
