If you're a Sideline Pro subscriber, your contacts will not sync with Sideline Web Messaging. Any changes you make through the app will not show in the Web version and vice versa.
Furthermore, you are unable to see and/or use the Contact Panel (available for Pro iOS only) in Sideline Web Messaging.
In order to save contacts on the Web, you will have to rename the Contact. More information on how to do this can be found here: Intro to Sideline Web Messaging
If you have further questions regarding how your Contacts are displayed, please submit a request.