I re-reported this issue at the beginning of the spoiler season when it was announced untapped triggers were a thing. What Sloth said is exactly right. If a trigger would happen during a phase where no players would receive priority, those triggers are "held" until a player could receive priority.
This basically translates into: "All triggers that happen during the untap phase and all triggers that happen at beginning of upkeep need to be added to the stack at the time the upkeep ones normally do: at the beginning of the upkeep. Follow normal APNAP rules for ordering."
I had that portion of it working a few months back, but I ran into an issue where for some reason upkeep triggers were triggering twice. Somehow during the adding of triggers, the trigger was firing again somewhere in the stack trace, and thus being added twice. Between
Hollowsage and the scripted Inspired cards, there should be enough untap triggers for you to see what's going on. Watch carefully and you'll see that the trigger goes off during the untap phase (trigger on the stack, input box says Untap). The whole paying mana part doesn't actually make a difference, if those cards trigger in the Upkeep without the normal Upkeep triggers being messed up. (I believe
Blastoderm was the card I noticed causing me issues, but I'm sure there was probably others)