DevTest considers HTTP as the transport and REST as the data protocol; therefore, the transport is all DevTest needs to get a request from your client to the provider application. This is one reason you do not specify a REST DPH until you have completed the recording and you are configuring the Recorder to process the payload part of the transaction.
What port did you set the recorder (i.e., Virtual-Ipaddress) to listen on? This may be why the request timed out.
And, did you configure SSL settings in the Wizard when you defined your target host and port.
Check out what Bhavin did in this videos:
-- In this video, look at how Bhavin set the recorder to use SSL. In this example SOAP and REST are treated the same. I believe Bhavin used port 8443 to demonstrate SSL.
-- In this video, Bhavin points our more about the REST protocol itself and how the URI is parsed.
In the first video, pay particular attention to the 'Use SSL to Server' and 'Use SSL to Client' settings. Since you are trying to record SSL (HTTPS), you should identify to the Recorder that you need the traffic encrypted. If you leave the keystore files defaulted, DevTest will use what amounts to the same encryption that a browser uses when it sends transactions to an HTTPS endpoint. If your server is using a custom certificate, then, as Rick pointed out, you need to acquire a keystore from your admin. My assumption at this time is that you DO NOT need a custom keystore file.
SSL with VSE Recording - DevTest Solutions - 9.1 - CA Technologies Documentation - There is also some discussion here that references SSL.
Assuming you can use SSL OOTB, try this configuration.
Your client sends its request to the Recorder on port 8080
(https://Virtual-Ipaddress:8080/services/supplychain/customerordermanagement/orderdetail?OrderNumber=212341234&NodeID=1234&Country=US)
The Recorder and the Client handshake and use SSL.
The Recorder sends the request on to test-services-customer.lawtram.com on port 443. URI info passed on to this endpoint.
Since Use SSL to Server is checked on, the Recorder acts as the client and exchanges DevTest keystore information to determine the encryption algorithm.