Thank you Martin - that helped a lot!
Here is what I had to do for Omnisphere specifically:
1. In Omnisphere, right-click the control I wanted to automate and choose "Enabled Host Automation"
2. Open Automation Mappying, click Add Entry, click L for destination and move the control in Omnisphere
3. For source, I chose a MIDI CC number in the appropriate MIDI port / channel
4. In Pro Tools, I automated that specific MIDI CC number for the appropriate instrument track that corresponded to Omnisphere (MIDI port / channel)
A few follow-up questions:
1) What are the "parameters" for in the Source automation mapping dropdown? How do those work with the host or should I only use MIDI CC / Learn?
2) A Pro Tools specific question - do you happen to know how to rename the automation parameter in Pro Tools? I assigned it to MIDI CC 20 in VEP, which shows up as "Unnamed" in PT.
Thanks again!