It prompts the first time you open the app (per install), then saves whatever choice you selected and doesn't prompt after that. I'm not sure exactly what your testing conditions were, but that's my experience.
Someone on that Adobe support post recommended I use the Cordova CLI, which DID NOT produce the prompt, leading me to believe it is a problem on Adobe's end. Of course, this build produced a sound bug that I've had little luck troubleshooting, so I'm still not really any closer to having my app updated.
I tweeted at Adobe Support and they weren't super helpful. The rep on that support post recommended I make a ticket for it, so at least they're pretending like they believe it's their problem (5 months ago, when that post first came up, the rep pointed the finger at Construct).
I'm writing the ticket now. Hopefully something will be done in a reasonable amount of time. I'll also try rebuilding my game to see if it's randomly working as you described (even if it's sporadic, if I can get one good build I could push my update).