This is basically like a very small jetlag issue. Your basals are tied to your 24 hour biological rhythms. One is sleep, there are others that go with the ebb and flow of the day. It makes sense that if you have dynamic basals and you move your pump settings back or forward an hour, there might be some mismatches until your body catches up with the new rhythm. Which should hopefully be just a couple of days. That said, just changing the pump time should be all that is needed. I suggest if things are problematic, change the time on your pump more gradually from the basis of your established body clock to the new time. For example
Day 1 10am on pump, 10am other time
----- Daylight savings hits ----- (hour forward)
Day 2 go forward 30min to 10.30am on pump, 11am other time
Day 3 go forward 30 min to 11am on pump, 11am other time
You could do the "day 2" scenario for a few days. Or do it in smaller increments if you really feel the need. Just don't use your pump time to go to any work interviews!
If things are going right out of whack, and things don't settle down in a few days, I'd suspect coincedence with getting sick or something else.