I like Green's answer. I'll add a few details I think your birds would have.
The way their symbiosis happens with humans looks like what happened between wolves and the first humans in our world. Neither species "needed" the other to survive, but where both met and cooperated, they fared better than they would otherwise.
The difference being that in our case, wolves are docile enough to be domesticated. Your birds seem too large to be easily leashed and dominated by force. Their social behavior may also not include an alpha in a group, so a human wouldn't necessarily be able to command a pack by bonding with its leader.
Bonding with these critters is not going to be as easy as bonding with a wolf. It also won't be the bonding a tamer has with a lion neither. I'm saying this because I think humans don't get to raise them from youth, right?
Still, a relationship like the one you describe, where it seems to me there is no master and no tamed beast, is not unheard of.
In Brazil, wild dolphins have forged an alliance with fishermen where the cetaceans call the shots. This makes the hunt easier for both species. This has been going on for generations, with the adults from each species teaching their young how to play their roles in this partnership.
So there is a model for you to develop on. It could go something like:
- Humans build traps to catch prey, but the catches are few because we are poor runners (when compared to game);
- Birds, on the other hand, cannot build tools and traps, due to an accute lack of opposable thumbs, paired with a less powerful brain than ours. So they have to rely on talons, sharp beaks, maybe even teeh like the most primitive birds, and a lot of blunt force;
- At some point, birds learn that they can save themselves a lot of effort by leading their prey into traps built by humans. This involves some trial and error before they figure it out, but they eventually do;
- For the first few dozens of generations, humans and birds fight for the spoils. But some birds notice that taking some flesh and leaving another part for the humans is less of a hassle than fighting them.
- Humans also notice this. And they tend to set up traps more often where they live close to bird populations that won't fight them for food.
The very first trait the birds have to evolve is the ability to recognize humans as something other than food or threat. If they can communicate with humans somehow, it will also be to their advantage - like a call to tell us that the prey is coming, so we can activate a trap somehow. Or a call to signal which direction they are coming from.
If they can learn to distinguish signals given by humans, i.e.: a hunter saying "nonono" while pointing to where a trap sits, so they can avoid it - that will also be to their advantage. They will learn to read cues from our voice, facial expressions and hand gestures, much like the way that dogs can read us.
This hunting strategy also benefits them more if they hunt as a pack, so that they can coordinate among themselves how to better push prey onto traps. This may actually how and why they evolve to move in packs, with the populations of birds that don't cooperate with humans living a more solitary lifestyle.
Since a pack is more efficient in killing prey than a single individual, the members of a pack don't have to be as large and strong, so they may evolve to a smaller size - which may be part of the reason that pack hunters like velociraptors tended to be an order of magnitude smaller than solitary hunters like the T-Rex. In your case, it could be that two and a half meters being the final size of your human-friendly terror birds, their closest cousins may be four-meter tall solitary terror birds (or whatever larger size you decide to settle on, if you wish to include these details in your world);
Now say we cooperate to catch the bigger, meaner beasts out there (mostly bull-sized or bigger mammals), but your birds can catch rodents, lizards, small cats and birds etc. on their own. They will lose some traits they need to kill off the larger, harder game on their own. They may evolve to lose their teeth (if they have it), and their talons and beaks may lose some sharpness. They will still be sharp, just not as much as originally. Maybe they originally had claws like a velociraptor, and now they have claws like an ostrich. Their beaks will still be sharp, though, at least as a vulture's, so as to cut flesh in smaller, swallowable pieces.
As to how the birds become mounts. This may be awkward.
For an animal the size and shape you describe, the only reasons another creature may want to climb its back and cling there would be to kill it or to mate with it. We know that the riders don't want that, but how did they convince the birds to allow themselves to be mounted in the first place?
It may be that the mother birds carry their young in their backs. That's why they would allow a human, specially a small one, to climb there - they have the instinct to carry another creature there (maybe only fmales are rideable? Maybe that's why women bond with these birds more easily?). At some point someone had the idea to mount a bird to use it for speed on a hunt, while taking along some javelins or a bow. This becomes a successful manner of hunting, so the birds evolve into a more ostrich/chocobo body shape (i.e.: more saddle space, wings don't interfere with leg riders so much).
But for this to happen, it may be necessary for them to learn how to live along with humans first. Such as in the way described above in which they approach humans for an easier, but with no mandatory close contact.