Where is there any requirement for the refuge side of a horizontal exit to be equipped with standpipes? It's not in IBC 1026.4, and it's not in the definition.
Yes, it is understood that the exit doors from the refuge side are sized only for the original occupant load of that area. Doesn't matter. The whole point of a horizontal exit is that it is the EXIT from the fire side. Once those occupants have passed through the horizontal exit, they are considered by the code to be out of [immediate] danger. True, the capacity of the refuge area has to be sized to accommodate both occupant loads ... but it's sized at a ratio of 1 person per 3 square feet, which is denser than any normal occupant load for any occupancy.
The code tells us that the occupant load from a story above or below is NOT added to the occupant load of the story of exit discharge. "Converging" occupant loads are added only when the level of exit discharge is an intermediate level, with egress from the story below the level of exit discharge and from the story above the level of exit discharge converging at the level of exit discharge.
How is an exit stair from above discharging into the refuge area of a horizontal exit? That's an entirely separate question, and I don't see any way it can happen -- irrespective of convergence (which doesn't apply). Once in an exit enclosure, discharge from the enclosed exit can only be directly to the exterior, to an exit passageway, or through an exit lobby or vestibule IF it meets the specific requirements for same. A stair from an upper story that dumps into a space on a lower story isn't an "exit," it's a convenience stair.