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.
No, Delphix won't install anything on source/or target only you need to copy the toolkit and check the prerequisites.. Like delphix user, read/write permission to mount point, sudo privilege to delphix user to mount, unmount the file system, read permission to /etc/oratab... etc.
Toolkit , is some of the delphix written shell /rman scripts.. which do the rman level0/ level1 backup scripts... while you are configuring the Delphix ---dSource which have the details of Source server name, username, password/ dbname etc.. with that it connects from Delphix engine to SourceSever/dbname to get the db changes ( level 0 initially one time) after that it take level 1 or incremental backup/or archivelogs backup to delphix engine..
Target also similar.. you need to configure in delphix engine where your vDB to be created -- like server name , osuser. dbname , mount point etc.
When you are provisioning a vDB all the above details are required ..