Hello Ihaveaquestion__,
Thank you for posting to Apple Support Communities.
We understand you have a question about syncing iCloud calendars. Is that right? If these imported calendars are calendars that are synced from services other than iCloud, this is expected behavior. These are services such as Microsoft Exchange, Hotmail/Outlook, Yahoo!, or Google. iCloud calendars sync between iCloud and your device.
However, if what you mean by imported calendars are imported calendar events into your iCloud calendar--these should sync as iCloud would. These articles can be helpful:
Keep your calendars up to date and share them with iCloud - Apple Support
Set up mail, contacts, and calendar accounts on iPhone - Apple Support
That should help. Let us know if you have any questions.
Take care.