I wonder if this is a borrowing from German (die Kasse)
More likely directly from Polish "kasa", but it's related to German Kasse, no doubt about that. Ultimately related to Latin capsa (a box, repository).
According to Wiktionary, German Kasse comes from Italian cassa, from Latin capsa. Ukrainian каса isn't in Wiktionary (not a lot of Ukrainian is), but the Polish route certainly seems plausible.
"The cashier is there." should have been accepted. We use this sentence: "Каса там." around the world. I'd never have known they were refering to a 'ticket office'. We'd use "бюро квиток" or "будка квиток" if it's just a 'ticket booth'.
Cashier = касир (the person)
Каса can mean a cashier's desk, a cash register (the device) or also a ticket booth (e.g. to buy train tickets or concert tickets etc.)
would "ticket booth" or "ticket desk" be correct translations here? i accidentally said ticket desk instead of office and got the question wrong, but would have thought its the same thing