Of course he has to grovel.
Grovelling is cheap. Grovelling doesn't cost mana or spells or trade goods or anything else they need to get everyone out alive. Wars, on the other hand, do.
He considers his approach. He understands that the Anglos don't bow-- most of the Sinos don't anymore either, outside of formal situations-- but they know Shanghai is traditional? Perhaps they'd be insulted if it were excluded. It's probably better to err on the side of abject humility. (Grovelling is cheap.)
It would be rude to approach Annaka with this directly. Shanghai doesn't want to imply that so petty an issue as some minor detail about Shanghai's alliances is worth her time. Unfortunately, it turns out that Shanghai also has no idea who New York's second-in-command is. This is an oversight they're going to have to fix in the future, it's a few days after graduation but that's not an excuse, Meng Yao is supposed to be omniscient. They decide that grovelling at Annaka's sister is probably good enough. They wouldn't take offense at someone grovelling at Lan Wangji, and he would certainly refer them to the correct person to grovel at.
So Julia is sitting at the library when suddenly there appears a small, very pretty Chinese man who kneels at her feet with his head on the floor and says in nearly perfect English, "this humble servant would like to request your tolerance of his apology for the offense caused by Shanghai's ally."