Hi,
On a target server, its pretty easy, there will be NFS mounts from the Delphix Engine mounted on the target server ( assuming a *nix target, windows with have iscsi devices from the engine ).
On a source server its a little bit more difficult, a few things you can look for though,
1. There will be a Delphix toolkit directory somewhere on the host
2. Assuming this is oracle, you can query the v$backup_files view to see if any backups have a tag like 'DLPX%',
3. Again, assuming oracle, you could look in v$session or dba_hist_active_sess_history for sessions coming from the Delphix Engine.
4. You could look for network traffic/connections to the Delphix Engine.
In both cases though, the best way would just be to login to the Delphix Engine and look at the configuration.