Calories are tracked throughout the whole day, by monitoring your heart rate, regardelss whether any MoveIQ event was detected, or regardless whether you started any Activity manually, or not at all.
If the data shown by your watch does not appear in the Garmin Connect account, there are basically three possibilities:
When the synchronisation works (the white sync circle closes and turns green), but not all the data is appearing in your account, then it very probably means that your device is associated with multiple accounts, and a part of the data lands in the other account. It frequently happens for example when you reinstall the application, and inadvertently sign up a new account instead of signing into the original one. Follow the instructions from the support document Data is Missing from My Garmin Account After Syncing to resolve the issue.