Whilst we can pull the team of a project, in 15.1 doesn't appear we can pull all the project allocations a resource is associated with.
curl -X GET --header "Accept: application/json" "http://MY_SERVER/ppm/rest/v1/projects/PROJECT_ID/teams"
Also I believe use of the rest API is not supported at this time.
So I'd advise going through the webservice route, i.e. create a simple NSQL query with a user parameter