updated_time and created_time are internal properties used for sync and to know when a note has really been created, so they should not be set and their value will probably be ignored anyway.
user_updated_time and user_created_time is the value you see in the UI and what you’ll want to set. That being said, I haven’t thought of the API as a tool to import archived data so I’m not sure these properties are handled correctly. I’ll have a look.