Going by Ansem never using the Guardian again past the scene in Twilight Town with it throwing Hayner away, using new dark energy attacks instead in all fights he appears in in the keyblade graveyard, both it and Terranort's during the KG battle must be one and the same - so we can safely say Terra's Heartless is not time-travelling at least.
What seems to be going on is that when Ansem (Xehanort's Heartless, NOT "Terranort"'s Heartless, as we now know) got destroyed, Xehanort's heart went back to his body he cast away during BBS. At this point, Master Xehanort should already be back but let's assume Riku genuinly had part of Xehanort's Heartless left until the explosion in KH2, preventing MX from reforming until then, which puts it close enough to Xemnas's destruction in the timeline to work out fine. (and not just "MX wasnt thought of yet")
Then, Xemnas (Terra's Nobody, but with Terranort's memories) was destroyed, and thus Terra's body was "free" again, ready to receive his heart...
Except, Terra's Heartless was never destroyed - it lived on near Riku who still held a piece of Ansem inside of him during CoM/KH2, and then it went back to Ansem when he started time-travelling.
So, back to KH3, Terra's body is now without a heart, because it satisfied the conditions to return due to its unusual state when it became a Nobody - it is now an empty vessel much like comatose Ventus in CO/LoD. Completely free for the taking by MX.
And you know what, I think we see the empty Terra without a heart be overtaken by a fragment of MX's heart in REAL TIME. Why would Terranort suddenly not have white hair or gold eyes anymore only to regain them a few seconds later? When the whole thing is the sign someone is overcome by darkness or Xehanort in this case, it seems rather suspect you can suddenly just straight up "hide" it to trick people. No no, that actually WAS terra's (empty) body, up until Xehanort took hold of his last vessel, put there BY xehanort who would enjoy nothing more than to give our heroes some false hope.
That additionally explains Ansem using Terra's Heartless just fine all the way up to the KG fights - Terranort simply did not exist yet as he was made like minutes before the actual "second" keyblade war began, so Terra's Heartless had no one else commanding it.
Here's a fancy flowchart that actually makes perfect sense
https://puu.sh/CJSlk/2de10d0ce6.png