If that's true, it's pretty interesting, maybe the FE characters have different "Smash" versions of themselves after all.
I remember something called Smash Brethren in Awakening too.
What about Manaphy?
It doesn't have a tail and it's definitely not a firefly XD
Basically, to explain this confirmation, all of the amiibo characters in Fates essentially say they were pulled from a world where they "battle many champions". Robin and Lucina are more direct about it, with Robin's last memory being "I was launching the other fighters...or were they launching me?", and Lucina saying she had just had a victory and was being applauded by her opponents before she arrived in Corrin's castle.
They also are all notably "battle obsessed" in Fates, which isn't really a trait they had in their own games. Ike is literally Ryu and wants to "fight the strongest opponents" Corrin's world has to offer, and Robin seems to think everything is a battle tactic in some shape or form.
Other OoC traits with Robin and Lucina in particular, is that Robin is much more aloof and distant than he is in Awakening, while Lucina is much more cheery and gentle than she is in Awakening.
The REAL kicker though, is the special conversations you can have with Lucina and Robin, if you take Laslow, Selena, or Odin into the Hero Battles with them, and let them fight Lucina or Robin. Doing so triggers special conversations.
Laslow, Selena, and Odin are all time/multiverse travelling characters from Awakening that return for Fates as part of the main story (and went by the names Inigo, Serena, and Owain in Awakening), and as such, they all recognise Robin and Lucina. However, upon conversing with them, they come to the conclusion that "you seem a lot like Robin/Lucina, and look exactly like them, but I don't think you're the same one I know...". Which is a blatant confirmation, the Robin and Lucina in Fates are not the ones from Awakening, they are the trophy champions from Smash, and we can naturally assume Marth and Ike are the same too.
Another thing to note is that, while Lucina remembers Laslow, Selena, and Odin, and by their previous names too, Robin does not. If Robin was the one from Awakening, he should remember who those three are. You could argue "maybe Robin was pulled from BEFORE Awakening's events", but this doesn't work - Robin's default class in Fates is the Grandmaster class, at Level 15. In Awakening, Robin is a Tactician by default when you begin the game, but Grandmaster is what he can be promoted to if he reaches Level 10 and consumes a Master Seal.
Even more is that Fates has day one DLC for a map called "Before Awakening", which is, literally, Corrin and friends showing up before Chrom and friends, and they help each other in a fight against some otherworldy soldiers. At the end of the map, after Corrin returns to his own world, and immediately after, Chrom finds Robin laying in a field, leading into Awakening...except when I did this map, Robin was one of my units too.
So basically, logically, Robin should not have amnesia if he was Awakening Robin - since he is a Level 15 Grandmaster when you fight him and recruit him, he would have to remember the characters from Awakening if he was Awakening Robin, since under Awakening's terms, he would have to have progressed into that adventure quite a bit to be a Level 15 Grandmaster, and should remember at least one of those three time jumping characters. The only explanation for Robin being a Grandmaster and still not remembering anything, is that he was pulled from Smash (as he directly implies he was), and that Smash Robin is a different person, likely just a trophy brought to life, as Smash lore has implied since Melee.