Yes, Momento does support timezones. It will detect timezone changes automatically based on your device settings. Timezone changes are displayed on the day timeline.
Items imported from feeds will be imported with timezone information if it is available from the original source. If timezone information isn't made available from the original source then Momento will use the current timezone (based on the device setting).
We do plan to improve timezone support using location data associated with a moment. When these changes are made existing moments will be corrected.
Can timezone information be corrected or added manually?
Not at present but this is something we're considering for the future.