Internal connections to servers from corporate networks are unaffected.
While the bug has been documented by Cisco, the bug itself is not Cisco-specific and affects other clients, even iOS's own built-in VPN client.
We have noticed a couple of OS regressions between iOS 8.4.1 and iOS 9 which have been reported to Apple. Most notable is that when doing Split Tunneling, the Tunnel All DNS option no longer functions as expected. This was reported to Apple under Radar # 22558059. This is not resolved in the iOS 9 release.
The current beta release of iOS 9.1 is also affected.
If you've upgraded to iOS 9 and you can't wait for Apple to fix this issue then your only hope is to roll back to iOS 8.4.1. But there's a catch - you can only do this if you made a backup of your device via iTunes (not iCloud) before carrying out the upgrade.
If you do have an iTunes backup then connect your device to iTunes and then Alt-click/Option-click the Restore Backup button from the iTunes Summary window. Now go looking for the appropriate .ipsw backup file. Hopefully, iTunes hasn't been "helpful" and automatically purged it from your computer to make room for a new backup. If it has then you might be able to recover it from a backup.
If it has been purged, or you didn't make a backup before you upgraded, then you can download the applicable file from Apple (links available here), but bear in mind that your device will be factory reset if you use this file.