I feel like spacing yourself to be in an intimidating position offstage against someone coming back is a lot easier because there's a lot less options people have there. They have to be coming back in towards the stage for the most part. They will have to double jump at some point depending on how far they are coming from and how much pressure you are putting on them. If you can pick up a habit for when they tend to burn the double jump you can catch them right out of it and they're pretty much dead (depending on the character of course).
I'd say my offstage play relies a lot more on reaction than reads though. Often times as long as you position yourself in a threatening enough position where you're just outside their range of attack, but in range to quickly double jump into an attack of your own, you can just wait for them to push a button like air dodge or throwing out an attack and immediately jump into it to punish it. You of course sometimes should mix things up to keep them on their toes and just go in with the attack so they know they actually do need to air dodge sometimes. So there's a mix of conditioning things you can punish easily on reaction and taking some risks with aggressive attacks. You just need to be extra alert when you take the risks offstage to not put yourself in a position to get spiked by their punish if they read it correctly and also be prepared to tech any stage spikes if your risky move fails as well. Also realize how little it takes to gimp a recovery. A lot of times with falcon I go out with a knee intentionally not really spaced to sweet spot just to have a hit box out to cover some options and just give people a tap to push them away slightly after they used their double jump. Because a lot of people tend to recover low and just enough to get to the ledge with their up b, that little tap is enough to make them unable to recover. It might not feel as satisfying, but it gets the job done.
When you're coming back yourself against someone you have to keep all of that in mind as well and react to their spacing by spacing yourself and reacting to what they do. Try not to come back in the same exact way every time and let them pick up on your patterns. Always choose very carefully when you burn your double jump(s) as you lose a lot more options when you get hit offstage again without a jump regardless of what character you are. If you realize the other person tends to come after you in the same way multiple times, be prepared to turn it around on them next time and punish them for it, but still account for the possibility of them trying to condition you. Like a lot of the times that you came out after me with your d-air as samus, it seemed to always be in a consistent spot so I was pretty much always punishing you with a b-air on reaction whenever you tried. You should only go for spikes like that when the other persons options are limited enough that it will cover enough of their options without putting you in a bad position immediately if they dodge it.