I just figured out that it is possible open specific page using IE which is perfect for me.
All I need is to use following syntax:
C:\Program Files\Internet Explorer\iexplore.exe https://www.some_page.com
It works well, but only in case you are trying to establish VPN connection manually. In case you are already connected to some other site, and your VPN client will automatically connect you to site where Post Connect Script feature is running, it will not open the page.
So it would be nice to have also this "bug" fixed, if possible somehow