well...to be fair...
To say a "house is unbound to time" sound as sci-fi or magic as saying "April travelled in time". But the games do speak for themselves: April clearly doesn't travel through time, at least not willingly.
Saga is April reborn and she knows April will show up.
Saga does perceive the passing of time. In fact:
1. she knows she will die (and we've watched her whole life in the course of 5 books)
2. she says that it's not really a circle but more like a spiral
I think the last one means time does go in circles but it's got a beginning and it's set to end.
That implies a preset path (which echoes through time) and a divine providence at work. The strongest clue is Saga knowing everything that's bound to happen because of song-lines.
My point of view is...if the house truly was unbound to time, the it wouldn't have been built by Magnus and Etta and/or Saga would have no age...or maybe she wouldn't age while in the house. So: time does not affect the house but the house and its inhabitants did have a beginning and will have an end. Time is a spiral.
poetry: this is where this game shines!
Yeah... umm... what about the part where they clearly spelled out in exactly as many words that the house of all worlds is unbound from time? Shall we just pretend that it didn't happen because we don't like it or don't understand it? There were precious few things that Ragnar and Dag went way out of their way to make extremely clear throughout the TLJ saga, and this was one of them.