With Sonoma, Apple introduced a two-level access mode for third-party apps to calendars. Open System Preferences and under Privacy & Security > Calendars > Export Calendars Pro > Options, make sure "Full Calendar Access" is selected.
An update of Export Calendars Pro updated for macOS 14 Sonoma will support the new access modes directly in the app.
Export Calendars Pro uses a dedicated application programming interface from Apple to access calendar data. Only calendars and event properties supported by Apple's Calendar app can be exported with the app. As a consequence, the app works with third-party calendar apps to some degree:
Most likely, the "wrong" time zone (almost always GMT/UTC) is tied to those events, presumably without your knowledge. Often, there is also no time zone set in the event. Apple Calendar assumes GMT then and passes this to Export Calendars Pro.
Solution: In your Export Calendars Pro export template, open the format menu for every date/time and set the time zone mode to "Use current time zone".
Hint: If you want to check or edit the time zone for an event in Apple's Calendar app, time zone support has to be enabled. Choose Advanced > Turn on time zone support in Calendar's preferences.