The 3rd party server needs to send a RADIUS Access-Challenge to the NPS server. If your 3rd party service isn't providing that, then the VPN client will never see that from the NPS server to present the extra login prompt.
With SMS (and voice/call), this usually doesn't work, as the two services are out-of-band of each other (the RADIUS server is effectively hanging while waiting on the 3rd party to respond).
If you believe it should be working, then you'll need to run a VPN debug on the gateway to watch the RADIUS session between the gateway and the NPS server.
For a quick debug, you can just do a "tcpdump -xXvv -nni <interface facing the RADIUS server> port 1812" and look at the RADIUS packet decode (access-accept and access-challenge is what you want to see). If the tcpdump isn't helpful, then you'll need a VPN debug.
Regardless, I wouldn't expect this work.