When opening Tools & Settings > Application Vault there are no applications in Installed Apps and My Apps tabs. Why?
Application Vault performs the functions of a local repository and an apps management tool. If there are no applications listed in Tools & Settings > Application Vault > Installed Apps or Tools & Settings > Application Vault > My Apps it means that there were no attempts to install any application on the server.
More information about Application Vault can be found in Plesk documentation.