I am currently writing a "time-travel" themed story that is more of a first-person perspective of all involved characters, and I want it to include the before and after reactions to the "time-travel" event.
So as an example, the reader gets a look at the perspective of the time-traveler, perhaps preparing for his jump, then using a "meanwhile" jump, we look at the perspective of the audience to the time-travel event, where the time-traveler arrives.
John was uncertain about this; he'd run his tests, and everything was positive, so there shouldn't be anything to go wrong. But just like the vertigo you get when you bungee-jump, you know it's safe; they've done it time and time again so you know you aren't going to be harmed; that fear keeps you from immediately leaping. "Damn it all." He said, jammed his eyes shut, and slammed the button.
Meanwhile, on the edge of the Paleolithic-era jungle, the tribe of cavemen sat arguing (well, I say arguing, more just aggressive pointing and grunting, and drawing in the dirt) about... well, something. Nugba (that's what his mate called him) could never quite follow these arguments. He thought they were arguing about food, but Grund and Fuh seemed to be getting very personal about where it was ok to pee.
Nugba was about to shout at them to try and bring the topic back to food, when suddenly a flash of light and heat blasted from the center of the circle, and a creature dressed in black shiny rock and hide that flowed like water stood there. After the dust settled, it spoke. "Hello there, I'm John."
In that situation, "Meanwhile" kind of works, provided it's followed by the context of the situation we're jumping to, and while in my head and in the context of the story, it's technically correct, because the idea is that all time is fluid (without going into further detail; whenever you want can be now, then, earlier, later or sooner), is there another phrase(s) that could/should be used for this instead?