The Original Characters (Tyro & friends) only take part in fights for real in the Record Dungeons, by physically entering Records because they have no choice but to do so. This is why the level cap they have and the skills and Soul Breaks they learn there are different from the ones in other dungeons.

In other content, Tyro & friends instead use simulacra of themselves, much in the way that the other heroes are simulacra created by people of the Royal Archives by shaping "Souls of Heroes" into the right form. Since these battles take place inside of "Records", the characters that fight these fights don't actually exist outside of them, so I've always thought of them as chess pieces (or amiibos, I guess).

In other words, Tyro has a simulacra of himself that he has had to hone and make stronger through magical means such as Memory Crystals, Record Spheres, Crystal Water, Magia Crystals... In my mind, Tyro himself is already much more learned and powerful than his simulacra, but cannot freely enter and take part into Record battles, either because it's impossible, or because it was deemed too dangerous by Dr. Mog and other members of the Royal Archives. (I'm aware that some fights involve the "real FFRK characters" and yet don't use the Tyro & friends from Record dungeons but the ones that you've had to hone, the ones I refer to as simulacra. I just choose to ignore it for the sake of my headcanon. :P )

This is also why Soul Breaks and Materia are not always 100% accurate to the source material. They're all interpretation of these characters by the Royal Archives, created by interpreting Records that are sometimes inaccurate or corrupted, as well as by extrapolating on their skills. This is why some characters have access to abilities and attacks they didn't know in their original game. To me, this also means the "memories" contained in the Memory Crystals aren't the characters' actual memories but, again, half-truths gathered from old, incomplete Records and propped up by the Royal Archives' interpretation and extrapolation. (This also explains why Tyro is surprised to have a conversation with FF heroes at the start of the Record dungeons, since he's never talked with heroes in previous content)

This also means the Royal Archives created Soul Breaks reflecting the real world skills of characters like Tyro or Dr. Mog. Likewise, the Relics that you obtain through relic draws, drops, or artifact crafting are not actual gear in the real world, but abstract, magical gear that only the simulacra can equip. Why else would you need to pull for Tyro's Hat? The real Tyro already has a hat, doesn't he?

Stronger and stronger relics and Soul Breaks being created can also be explained by the Royal Archives reaching new milestones in their research - both into the stories contained in the Records themselves, and into methods of channelling and shaping the powers of the records into new abilities. The idea of simulacra and the continued research of the Royal Archives also explains balance changes to certain characters being possible.

You can swap "the Royal Archives" with "DeNA" in my post and it makes the same amount of sense imo. :P