If I insert a synth via the Insert menu, that synth's audio output's Automation Lanes show up correctly:

 
However, if I insert via Track Templates, in this example, Omnisphere does not show up:
 

 
Has anyone come across this issue? (X3P)
 
 

I notice in the top picture, the popup is on the first audio track. The bottom picture shows the popup for the second audio track. There can only be one set of automation parameters for on instance of a synth. Is it possible in the second picture the automation parameters are associated with the synth first audio output?

Just tested, and no, it doesn't show up for the first audio out either.

Try assign the automation in the synth rack. If they synth rack is docked at left or right, select the synth and use the automation menu, "J" in this image

If the Browser is floating or docked in the Multidock there is an automation menu for each synth  "I" in the undocked image below

Thanks - I'll give it a shot in the a.m!

Worked!