As I understand it, every card that is not in a hidden zone, and that has forecast, triggers during its controllers upkeep.
So, each turn, everything (not in a hidden zone) that is controlled by the active player and that has forecast triggers (whether the card has any time runes on it or not).
If it has a time rune, then remove one. If one was removed, and it was the last, then it arrives.
‘Extra triggers’ from cards with Forecast and no time runes on them are generally ignored, as there is no ‘If no time rune was removed from this then do X’ clause, so the accepted shortcut is to not announce the triggers (and ignore them) but as best I am aware they still trigger every turn.
Edit: Maybe cards that aren’t in hidden zones and cards not in command zones (to allow for future heroes that might have Forecast) trigger during their controllers upkeep.