Insight have support for assign Insight objects to issues via the JIRA REST-API. Below you will find examples on how to do this:
This is supported from version Insight 2.24.0
As you can see below, you will have to use the key attribute to define the Insight object keys, when creating Issues with Insight custom field values.
All Insight custom fields are using ARRAYs of keys, even if you only work with single Insight custom fields. In that case, it will only contain a list of one (1) Insight object.