Although we do not provide REST API support for Power Custom Fields PRO at the moment, if you want to set certain values for a field using Jira REST API, there is a possibility. In order to do this, you need to use the same syntax as when setting a default value.
The value should have the following format:
{"label": "", "value": "<issue id>"}
Here you can see an example of how to use it:
{"label": "", "value": "10000"}
The field value provided to REST API should actually be JSON string of the given format. If you send an object formatted as described on the page, Jira will response with error message.