Hi, I had a similar problem when i try to save a post via the REST API.
The post is a custom post type with a type=date and timestamp=true.
I've tried to POST the field with date "Y-m-d", date "d/m/Y", datetime "d/m/Y H:i:s", timestamp format but or it stay empty or it takes 1 and show First January 1970.
Config
MB Rest API 1.4.0
Meta Box 5.3.8
WP 5.5.3