Clockwise runs by an individual's perspective in their calendar. Most Clockwise users work in a specific timezone a week at a time.
The best way to work around changing timezones is to flip the timezone as close to change as possible ahead of daily schedule optimization, and to create a day of blocks if you're working back-to-back without a day out for travel.
For example, if you normally work in PST and were working in PST Monday + Tuesday, then working in EST Wed through Friday, you would want to create an end-of-day block on Wednesday from 3PM-6PM PST to be sure you weren't working past 6PM EST.
You would then change your Clockwise timezone to EST just ahead of 4PM on Tuesday and remove that EOD Wednesday block that afternoon.
Because schedule optimization runs at 4PM daily, doing this before 4PM will allow Thursday optimization to run. If you change your timezone after 4PM, optimization would only run for Friday, or the day after your travel, because meetings do not move with less than 20 hours in advance to help you prepare.
If you're unsure of the time you changed your timezone, you can spot-check your meeting in the Planner view to verify if a flexible meeting will no longer move in the event history.