The article should add a caveat: use UNIX time when you are recording the current time to store for later use. That can always be formatted in the user's current timezone to display back.

When you're inventing a rule system based on local times, as you are above, of course you need to track the rules in the local time zone. That's because the rule is: "do this thing at 9am in my particular local time zone", not "do this thing every 86400 seconds". Keep in mind that this is hard, though, due to the fact that in many local time zones, one hour is missing on one day ("spring forward"), and one hour occurs twice on one day ("fall back"). If you have some event that should be triggered at 1:30am, which 1:30am do you mean? The first 1:30am or the second 1:30am? What about on the "spring forward" day, when 1:30am doesn't occur at all?