Looking at the VPN configuration I just imported from Hamachi into my iPhone it appears one of the signing certificates used by LogMeIn expired very recently:
LogMeIn, Inc.
Issued by: VeriSign Class 3 Code
Isning 2010CA
Expired: October 10, 2015
I've been having trouble getting On-Demand VPN to work and I was wondering if this could be at all related (I have read On-Demand VPN requires valid client certificates). I wonder if the expired certificate is what could be causing my phone not to auto-start the VPN when connecting to one of the configured domains in iOS 9.