The only question still open is why other devices draw 1.0A to 1.5A from my other charger, while the Gemini only takes 0.5A (0.47A to be precise)
Given how twisty the history of USB is, and the variety of how different devices interprets (or not) the various standards, I'm not too surprised.
My Gemini, even at a 70% battery level, pulls around 2.2A at ~4.85V from my (non Pump Express) 2A rated Samsung chargers.
Maybe your other charger thinks that's a bit too much and limits the current to protect itself, while your battery bank doesn't.
Or maybe the Gemini, for some reason, fails to detect that your other charger has a dedicated charge port.
Or maybe it doesn't have a dedicated charge port per se, and the other devices just tries pulling 1-1.5A anyway, hoping for the best.
Or maybe the cable you are using, causes more of a voltage drop at higher currents than the Gemini is happy with.
Or maybe the Gemini doesn't like your USB power meter.
Or, or... or.... some questions just doesn't seem to have have clear-cut answers.
You could try your other charger with the Gemini, using the shortest, fattest USB cable you can find and see if that makes any difference.
Or maybe you could try a few other chargers, when, say, visiting friends, with the Gemini, to see which does and doesn't supply >0.5A.