Everyone was expecting a huge reaction out of Twilight for this arc, and I get that's what we all want to see. Even I felt he'd have a bigger reaction to some part of it even though I highly doubted the "gonna run crying to greet Anya with a hug full of worry" reaction.
But honestly, his canon reaction makes the most sense. I think with all the fanon depictions of him, we tend to forget that Twilight has not cried since the war, that he is a spy that has deeply, deeply buried most of his emotions. This man is traumatized and is constantly trying (and failing) to stay detached from this family life because he still plans to one day leave it behind. And he achieves that by using his spy training to never acknowledge his true emotions.
And obviously some cracks have formed in this mask he's put up. But they're still so small. The most he let's himself feel in regards to his family so far is in those rare moments of relaxation with them. And the single time he almost let his anger get the best of him at the Eden interview. Yes, he gets anxiety around them a lot, but that's always in relation to his mission (or what he tells himself is part of the mission). Everything else he suppresses deep inside himself, never to be acknowledged. And that's all in the spirit of keeping a cool head.
He can't be super reactionary. If he is, the mission could be put in jeopardy. And also, he has yet to fully acknowledge any of how he truly feels.
So, tl;dr Twilight isn't at the point where he's going to cry over Anya yet and his canon reaction makes sense.