Welcome, @Samuel_Ward,
Rules shouldn’t be limited to Recently Assigned, unless you might have inadvertently specified that as part of the “When” or “Check if.”
Re your other point: Note that “Due date is approaching” triggers 1) only run once daily just after midnight, and 2) must match to the day exactly–so your mention of “within a week” is perhaps the culprit.
The help article you pointed to is not very detailed. Here’s my much more detailed advice that includes all the trappings and the exact specification of such rules. If you try these and they still don’t work for you, include screenshots and we can help.
Thanks,
Larry