I believe the HRD cookie will be created by ADFS if it is the IDP authenticated the user. In your case it seems that the user is authenticated outside of ADFS.
If users are always coming from the same IDP, you could customized the relying party trust to redirect directly:
Set-AdfsRelyingPartyTrust -TargetName TestApp -ClaimsProviderName @("CustomCP1")
I think there is an option to configure how the HRD will work between two ADFS servers (configurable with Set-AdfsclaimsProviderTrust). I'll try to find out more about that if the first suggestion isn't a good fit.