Imagine the Alpha trying to separate you and the Omega, thinking you were distracting him too much from the pack. And when the Alpha comes by, even does so civilly and tries to talk the Omega down and explains things to you, the Omega turns very aggressive. The Alpha is so stunned that they don’t even register it a challenge or a threat, they just stand there watching as you try to calm down your lover. Hushing them and stroking his cheeks, attempting to turn this around before it went too far.
And that’s when the Alpha realised that you weren’t a distraction. You were an anchor, a mate to someone in their pack. After that, you are considered one of them. Even if you are human. The Alpha still doesn’t completely trust you, but they tolerate you for their Omega member.