"Platform size matters a lot for this: FoD PS and Yoshi's ones are small enough for you to rest on reaction, and unfortunately you can't cover a techroll away from you on BF and DL with a rest (you can still follow-up though on reaction)
One very important thing is that Puff is the only character (with kirby) that's able to turn around in the air, and that's a very important tool
While her horizontal jump speed doesn't cover cover enough ground going forward, her turning back while jumping allows you to to cover more distance way faster
It's pretty hard to picture I guess, so just go into the game, jump at the middle of a platform then turn around while jumping again into the platform and it'll be obvious how much more space you cover
[Alex note: it is important to recognize that this is NOT because the backwards jump animation goes further or faster than the forwards jump animation. They are identical. However, turning around with a double jump immediately fully reverses your momentum, as opposed to jumping forward and then drifting back, which forces the momentum to transition from forward through neutral and to backwards over a period of something like a quarter of a second.]
I use that a lot to be able to cover a techroll away with a rest on smaller plats, or a waveland grab on larger ones
Actually that's how my set vs zhu ended: https://www.youtube.com/watch?v=sWUOdyJns1U#t=18m17s
The important thing to notice here is the arc I did with the first jump to position myself so that I could react to anything he did: I first went directly to where he was gonna land in case he didn't tech (which would have been an instant rest as I would have needed only to fade a lil bit more into him during his stun), then went right under the platform, from where I could have rested both tech on place and inwards, and finally jumped and turned around to pop right onto him after I saw him tech away
Keep it mind, though, that it does require pretty fast reaction time, so you better start practicing it right away! As mentioned, you should get/use 20XX and just upthrow fox/falco on small plats stages to practice the rest first, which is easier, then on the bigger ones where it'll get more tricky
I'd advise any puff to train to ALWAYS rest on reaction on small plats because it's just guaranteed, you have all the time you need. Bigger plats though do require some hard reads, but ONLY to cover techroll away, you can still rest tech in place and inwards on reaction
SO: positioning with the first jump (go a lil bit above the plat at ur peek then fade right under the middle while descending), turn-around jump, waveland grab on bigger plats (if you're not comfortable trying to read a techroll away)"
waveland regrab is necessary in the platform techchase flowchart because sometimes you start from too far to the side to DJ rest tech away.
But this is obv not the case in cases where you upthrow from the side to the top platform.
if you grab fox on a side platform and upthrow:
1) turn if necessary so that you are facing away from the top platform
3) if he DIs toward the top platform, FH that way, aiming to be underneath the middle of the platform at the apex of your jump (you will be facing backwards)
4) focus on reacting to tech in place or missed tech (he splits his legs in the air on frame 3/big green flash), double jump rest it if these happen
5) if he doesn't tech in place, FF at the apex of your jump for a few frames (the fast fall makes it so that as you come up through the platform you come up on top of him, not too high over his head. It is also nice because makes this an easier binary ("in place" vs "roll" reaction).
6) by the time you've done a slight FF you will know which way he is rolling. DJ after him and rest, should be a ~5f window or more depending on position/%/timely reaction.
This should be consistently doable vs any tech location on the top plat.