I have had a similar problem with the UpdatePanel and double postbacks. However these double postbacks occured in all browsers. I was able to finally figure out the problem and it was caused by double wireing up of the controls to the code behind event.
For example:
At the top of the page i had:
AutoEventWireup="false"
then my button:
<asp:Button ID="btnSave" runat="server" Text="Save" OnClick="btnSave_Click" />
then the actual code behind
Protected
Sub btnSave_Click(ByVal sender As Object, ByVal e As System.EventArgs) Handles btnSave.Click
The problem was that the button had an OnClick specified, and in the code behind it also had the Handles btnSave.click. By removing the Handles btnSave.click I was able to remove the extra postback. You could also change the AutoEventWireup to True and then just remove the OnClick reference on the button.
I hope this help
echo7