I think it's fine. I have personally grown weary of infinite multiverses and the actualization "every possibility" into a universe, so a limited multiverse is, at least to me, immediately more interesting than what many fictional settings have adopted as of recent. There's unfortunately not much else I can say on the idea, however. I'm of the belief that every facet of a story, including the cosmology, should serve a greater narrative, thematic, tonal, developmental, or philosophical purpose, so there's not much I can offer without context.
I am open to suggestions but I want a name that makes it clear that those timelines aren't real, compared to the main timelines. That name has to follow the rule of cool too.
I immediately thought of Quantum Superpositions as I was reading, oddly enough. I'm not sure if what I have in mind is entirely congruent with what you've proposed, but I think it's at least some food for thought: As possibilities, the "Lower Timelines" are simultaneously "real" and "unreal" until they either do or do not come to fruition, in the same way light can exhibit the properties of both a wave and particle until it is specifically observed. For instance, a possible "Lower Timeline" could be one in which the president of the United States dies "tomorrow" (in relation to the Main Timeline). "Today" the timeline is in a position of being both real and unreal, as there is a possibility the president could die tomorrow, though we do not which outcome will occur. If a possibility is actualized, the associated "Lower Timeline" becomes one with the "Main Timeline". If a possibility is contradicted or does not happen, it is "observed" as being unreal and thus does not exist. These possibilities, which I would refer to as "Schrodinger Timelines", are what compose the "Main Timeline".
I haven't thought of a good explanation that is interesting that would explain how those timelines can turn into main timelines.
In a similar vein to what I proposed earlier, there could exist an entity (character, object, etc) which has the ability to alter the ontological states of timelines. Through this power, one could transform previously-occurring possibilities to unrealities, reverting their impacts and implications on the "Main Timeline". One could also make nonexistent, "expired" possibilities into reality, causing separate timelines in which they did occur to form concurrent the primary reality and potentially threatening the integrity of the "Main Timeline".