The Owner field on roadmaps is not in sync with the Investment Owner/Manager field of a custom investment object. Do you need to create a custom field Owner on custom investment object to ensure auto-population of owner field at roadmap Items level?
The manager field is now available on Roadmaps and is able to be synced from investments. This field could be utilized instead of the owner field.
See the below screenshot referenced at Synchronize Roadmap Items with Linked Project, Custom Investment, or Idea Attributes that shows the attributes available for synchronization starting in 16.0.
You would need to create a new custom attribute on both the Custom Investment (or applicable object) and Roadmap Item object (with matching API Attribute IDs, Lookup data types, and lookups in order for them to sync). See Sync custom attributes from Project/Idea to Roadmap for steps on how to do this. This applies to any Out-of-the-box attribute where the API Attribute is in the old naming convention and un-editable).
Note: To copy over existing data, one option is to create a custom attribute and process, see the steps below.
See also: Roadmap known issues - master KB
For more details on getting started with Rest APIs, see: REST API Reference