For future events, you need to store at minimum the local time; of course, that's not super useful to use, so you may also want to store the UTC as determined by the best current information when it was saved.
Whenever you get new rules, you need to look at at least all future events and see if their UTC offset changed and then decide what to do about it. Often the right thing to do is just adjust the UTC offset based on the new rules; but sometimes you might want to ask the user, or maybe just notify the user: hey, we got new DST rules, please confirm these modified events: [list]. Users don't always input times accurately[1], so a heads up lets them review the modified dates and update the events that were modified in a way that doesn't reflect their actual intent.
You might also want to look at past events and maybe also notify users that the rules changed, and you're sorry about any inconvenience because you didn't get the rules or didn't process them until after the event.
[1] If I'm planning to watch a sporting event on TV, I'm most likely to input it into my calendar in my local time, but the event is most likely scheduled in local time at the event. But not necessarily. IMHO, the closer to the time change the event is, the more important it is to get user feedback.