Executing the process using the executeProcess action available in the AtomSphere API (either SOAP or REST) gives an HTTP response of success or failure but it does not return an execution ID. This is because the actual initiation of the process execution is asynchronous from the request to execute. The execution is asynchronous to handle situations such when the Atom is offline or is under high load and new execution requests are queued for some amount of time. This behavior is the same for manual execution requests submitted via the Process Reporting or Atom Management consoles.
The API for an executeProcess call will return an HTTP status code of 200 if successful. Currently it does not return a response with the executionId. To find the "status" of the execution, you can query the ExecutionRecord object based on query filters for accountID, processId, processName, atomId and executionTime as described at this link. The object returned will include a "status" field. If multiple records are returned, you will need to correlate executions based on executionTime query filter.
There is an idea for this capability here: executeProcess should return the executionId .