Our cat is starting to vomit a lot

I am catsitting two adorable boys for the summer while their owner is on extended vacation. One of them has occasionally vomited, no biggie, cats do that. A few days ago, he started to vomit every single night (and without fail, on or under my bed, thanks so much!)

He looks fine and healthy, has a cold nose, eats well, eliminates properly, and hasn't lost any weight. I feed them hairball-reducing dry food and brush both of them daily, so it shouldn't be a hairball issue. He does not properly chew his food though but rather inhales in the space of 5 seconds flat, but still, the daily vomiting is new, and he doesn't puke solid particles but brown liquid. He is 5 years old.

I tried to contact the kitties' owner to ask if that was normal but he is gallivanting around China so I guess he hasn't had a chance to check his email for a few days now. He expressly forbade me though to take any of them to a vet unless it's a real emergency. (I took one cat to the vet for a checkup after a fall/jump out of a third floor window, and the owner was pretty upset with me for taking him.)