The TMS WEB Core web client app performs the HTTP requests to the REST API directly from the browser. It's not going via the (local debug) webserver the app is started from. You give no information about your REST server and what technology is used for the REST server. But it is in your REST server you'll need to enable CORS.
Also, when encountering problems, open a browser console (F12 shortcut) as there will be more detail about possible errors there.