What happened to the timeline you left? It must still exist. You couldn’t have been the only consciousness that was experiencing it. To think otherwise is some extreme solipsism.
Why does it need to remain? It seems like solipsism to assume it must remain because it's your point of origin. If something or someone has the power to drop something into the past why wouldnt it overwrite everything? I don't see why consciousness even gets applied. The universe keeps on whether I am alive, asleep, or dead.
I see the path of time like a laser beam in a house of mirrors. If someone has the power to add a mirror somewhere. Yep, the whole beam after the fact is a vastly different pattern. Any multiverse would be entirely virtual and theoretical.
Oh I agree, it's horrifying. And I have noooo guarantee that it's me doing the jump. Don't misunderstand I am NOT the only real mind in this example. I'm curently just hitching a ride on said laser beam. No guarantees that I will be the same or even exist if somebody so much as moves a pebble into the past from the future.
Existential dread all the way. If we get time travel I think it's as horrifying a prospect as teleportation on a universal scale with only the traveller maintaining continuity.