I'm surprised that it was never mentioned at all.

Yes idk about supergirl 100% but Arrow 5x10 is immediately after 5x9
The flash 3x10 is about a month later

Are you serious bro?

Because the Flash is about a month ahead of Arrow and Supergirl's "time setting"

It was Andrea Brooks who plays Miss Teschmacher.
I think the scene with Vibe and Gypsy happened at night and the scene with Kara and Mon-El was in the daytime but it would have been cool to integrate the events of the Flash with Supergirl.
Maybe Kat will come back and complain about her coffee table being replaced, as she loved the one which was broken or it was a gift from some famous person she knows.

Well in the scenario I presented you don't see any actors, Kara and Mon-El stand there talking while waiting for Eve when they suddenly hear the table smash, walk to the room and when they get there they just see a breach closing. They could've even taken the short moment when the breach closes from the Flash episode.

It only costs money to put actors in scenes of shows in which they are not part of the cast. The only added expense would be breach CGI.
"I'm Wally WestThe fastest man alive!"

Remember, it cost money to put those actors in a scene, and the budget is limited. I wouldn't be surprised if the young lady we saw in the scene was a writer or girlfriend of one of the actors.
A person is never happy except at the price of some ignorance.
Anatole France (1844 - 1924)