Before we forget, Xigbar/Luxu was the one to "scout" Larxene and Marluxia for the original organization in the first place. The guy likely knew all too well where they would be upon re-completion, and could have easily gotten Xehanort to turn them back into nobodies on the spot. As for why they recall CoM, but not their real selves, a Nobody's memories seem to be tied to how long their Heartless existed for (see Sora/Roxas). It's entirely possible Xehanort dispatched their Heartless the moment they appeared so neither Larxene or Marluxia could recover any memories from their complete selves, merely retaining what they had from their time as a Nobody prior. This is without even assuming their complete selves aren't just amnesiac to begin with, which is very likely given Ven and Subject X's state.
This allows them to be current day nobodies again like Xigbar himself, Luxord, Demyx, Saix and Vexen, no time-travel involved, and with their memories the way they are (only Nobody memories, nothing else).
As for time travel itself, Nomura plays it fast and loose, but there is some internal consistency at play:
1) It IS possible for a time-travelling heart to manifest itself into the real world temporarily. This is done multiple times throughout the series, from KH1's Ansem confronting YX on Destiny Islands, to BBS's YX fight as the Mysterious Figure (Terra vs MF was deemed canon iirc), DDD's real org appearance, and KH3RM Sora's intervention during both the Terranort fight and saving the Guardians of Light in the KBG from the keyhole portals and an Armored Xehanort Replica.
2) A suitable vessel is required for a time-travelling heart to remain anchored to that time, hence the replicas needed for YX, Ansem, Xemnas, Vanitas and Riku Replica.
3) While time-travelling, your heart remembers everything you do, but to prevent paradoxes in its own lifetime, suppresses those memories (similar to how Sora will likely never remember CoM, but the memories remain in his heart). Why KH3 YX remembers DDD is unclear, but it seems likely that time-travelling again unlocks those suppressed memories.
4) No such memory restrictions apply to the memory of a heart from the future travelling to the past (and then back to the future), which is also precisely what the MoM was prepared for when Maleficent time-traveled to the age of KHUX as to prevent her from learning too much about the past, but since she knows of the box and the book of prophecies, he notably failed to contain her entirely (due to Darkness).
5) Stable time-loops with no determinate starting point can exist while still following all of the above, such as Re:Mind Sora being the reason normal Sora could beat MX in the first place (the destruction of Armored Xehanort in KBG weakened MX in Scala enough for SDG to overpower the X-Blade), or Ansem SoD being what set YX out on his path.
There's one thing that bothers me throughout all of this though.
How exactly are the 'norts time-travelling to the future to begin with? Ansem SoD had to sit around on Destiny Island for decades till possessing Riku, "as per the normal passage of time" after setting YX on his path, as described by YX in DDD. YX can seemingly jump to the future at will, and even has time stop/rewind powers for whatever reason, and he can pull other hearts along for the ride while time-travelling. He's also blatantly using a different method than the one described by Darkness in KHUX, which requires a machine (the Ark), a marker (someone that remembers you at your destination, like the 3 fairies) and a vessel/catalyst (such as Maleficent's cloak), because if he knew of this method, he'd just be able to keep coming back - after all; it's unlikely any of the main cast will ever forget him.