Start a session (see [man]session_start/man) and in the processing code, check to see if a certain session variable is set (whatever you feel is most descriptive). If not, do the UPDATE query and then set that variable.
How are you currently doing user authentication? In other words, once they login, how does that login information persist from one request to another? If you're using cookies, you could use the same approach above only using the cookie rather than using both sessions and cookies. Note, however, that any data stored in a cookie should not be considered safe against modification (malicious or not), thus sessions may still be a more ideal choice.
Also, note that you've got an error in your code snippet above:
if ($cat=2){
Here, you're assigning the value of 2 to the variable $cat. In other words, this:
if ($cat=2){
mysql_query("UPDATE tblCustomer SET logins = (logins)+1 WHERE CustomerID=$cust");
}
is equivalent to writing this:
$cat=2;
mysql_query("UPDATE tblCustomer SET logins = (logins)+1 WHERE CustomerID=$cust");