It sounds like your VPN is a split tunnel and your DNS is going to a remote server when connected to the VPN but regular Internet traffic is still routing via your local connection.
Because DTTS relies on DNS queries, and now is not seeing them this would explain the behaviour you are seeing.
There’s a few options. First is to have the VPN a full-tunnel, but then you loose the adam:ONE features unless you have it on the remote site.
In which case you may want to look at this article Active Directory Configuration which talks about how to configure an environment with AD and DNS.
The other option is to set the VPN server to not supply DNS so that the client end continues to use their local DNS server (adam:ONE in this case).