When a request come to ASP.Net it will create an object of that type and view state will help framework to set previous values of controls,Now in your case you have disabled view state for each label when button clicked it request to server without the value of both label and then server set respective values (as per your code) to the respective Label.
You have set your label default value to "Label" so other label set to that.
Now how to solve it
you can use two different update panel
You can use JQuery to achieve the same Link
Read below mention links you will find your answer:
Life Cycle Of ASP.NET
Ajax Update Panel