The default file system provider of the spreadsheet control takes a and excel file from the server and serializes it to the browser where the user can see and work with it in RadSpreadsheet. So, if you modify the file on the server, the next time a control instance requests that file, it will get the updated data. You can see this in action in our demos that you can download and run locally from your account, for example this one: https://demos.telerik.com/aspnet-ajax/spreadsheet/examples/overview/defaultcs.aspx.
If you want to display to the user something different than what the file contains, you would need to create a custom provider that will implement the desired loading and saving logic: https://docs.telerik.com/devtools/aspnet-ajax/controls/spreadsheet/data-binding/providers/custom-database-provider.
You can also administer changes in the browser through the client-side API of the control: https://docs.telerik.com/devtools/aspnet-ajax/controls/spreadsheet/client-side-programming/objects/spreadsheetrange. If you have a client-side event (e.g., fired by SignalR) that holds information about new cell values and their location, you can use that to update the user's current view. Note that this may result in data loss because you cannot guarantee that they have not changed some of those cells already.