With YourSites you set up your own private website then install YourSites as a extension. This website will run Joomla, but its easy to setup and once its installed you won't even notice what web software its running on.
This site can can be on your local PC, on an online server or even on an intranet or behind a firewall. There is no need to share your client data, or details of their sites with a 3rd party online site management service. The data is under your control.