If IE is open, your code works fine and opens each link in a new tab, if not, I was able to make it work by making the app wait for 1 sec before calling the second page to open:
void ReportingClick(object sender, EventArgs e)
{
System.Diagnostics.Process.Start("http://www.google.ca");
System.Threading.Thread.Sleep(1000);
System.Diagnostics.Process.Start("http://www.gmail.com");
System.Threading.Thread.Sleep(1000);
System.Diagnostics.Process.Start("http://www.stackoverflow.com");
}