It's not quite that clear cut. The only way the server can identify a "PostBack" is based on the headers passed to the page by your request. When you POST a form, "IsPostBack" is true, as you would expect. When you refresh a page or press Back the exact same request data is sent. There's no way for the application to detect that the user issued a non-standard request (Back or Refresh) without changing the behavior of the browser that sends the request.
As you know, most browsers will indicate to you that "Clicking Back will resend the form data...", but that is merely a warning issued by the browser to let you know that it is going to send the exact same request over again. The server does not know this and has no (native) way to interpret the information.
Double Postback Prevention Tips
One way to prevent data getting posted twice is to ensure that each PostBack contains some unique data that you can validate. The process is fairly simple.
On each page load you will want to create a unique identifier for that page's PostBack events. It doesn't matter what the unique id is, so long as it isn't the same on sequential page loads. Place that unique identifier in a hidden field on your page AND in the user's session (or a cookie). Then, on each PostBack validate that the cookie in the hidden field matches the value in the session. If the values match the PostBack is an original post to the page which can be processed accordingly. After performing the necessary operations you will then need to change the unique identifier in both locations again. This way, if the user should hit back and choose to "Resend Data", the hidden field will not match the session key and you can throw out the duplicate post data.