The thing about Ezra ... is that he possessed the ability to interact with the gateways which allowed him to use time travel.
"There are infinite paths and infinite possibilities but
*you* must open the door." - Palpatine to Ezra.
The abilities Ezra
can possess are what makes him a time traveler - to me. The Emperor couldn't open the gate but Ezra could.
Palpy needed Ezra to open doors for him - which Ezra denied.
(Also don't you think it was strange that Palpy was calling out to Ezra, similarly to how he does when he asks Vader for help? - Within the gateway. )
The Son (Mortis God) practically tells Ezra (through means of the Force) he has the ability to change fate if he wants to - when Ezra first seals the wolf gate.
The connection Ezra shares to living creatures (*Creatures that use hyperspace) could allow him to learn such abilities himself.
But in using those abilities he might become more than he is, as we know him as. So in a sense, to say ""Ezra isn't a time traveler"" is technically right. As "Ezra" is an Apprentice version of his potential. Ezra has to become a Master - someone he is not. So he has to become someone else. Becoming Kanan makes the most amount of sense considering some of the things Kanan says.
(Regarding Lothal)
Kanan: "Before we knew Ezra we were drawn here... [...] We kept coming back. "
Hera: "Are you saying we were meant to come here...? Maybe to meet Ezra?"
Kanan: [...] "Something like that. But there's more to it. I'm just not sure what. "
Around when the wolves start showing up, and Kanan and Ezra interact with them, Ezra asks Kanan; "So all the paths are coming together right?"
Later when the show is ending, Ezra mentions that there were "several paths" in front of him, and the events that we the audience witnessed, transpired because Ezra did so out of obligation.
The symbolism is that the Mortis Bird represents beginnings, and through a means of various paths and events, Kanan eventually displays Jaig eyes on his mask. (Kanan might not be the actual beginning, but he could be the BRIDGE for BRIDGER to avoid certain DOOM.) If Ezra pieced together that he had to become someone else, and learned how to time travel from the wolf (Himself/ The Brothers' Creatures.) he would have had to teach himself through Kanan. And to teach Kanan through the Wolf. (Lots of; wolf in sheep's clothing.) Essentially self teaching himself in the absence of a father. (Which he could have had but chose to find his own family - his own way - his own path.)
There seems to be lots of Individualism versus collectivism themes in Star Wars.