Magento2 get website_ids in product get api means product is assigned to which websites.
This is issue generated in github: https://github.com/magento/magento2/issues/5773 , but there still not any solution.
You could try this module because with this you can assign a product to multiple websites and retrieve it in the get API. I haven't totally tester the given case but I think it should work.
https://github.com/experius/Magento-2-Module-Experius-Product-WebsiteIds-Api
Let me know if this solved your problem.
