Don't you think that "I put ice into their cups" should also be an acceptable answer ?
That doesn't really sound right as a question. You would say 'Do I put ice in their cups?' or 'Shall I put ice in their cups?'
Yes sorry, the question was essentially focused on the "into". :)
I found some of the words' pronunciation a challenge. How about you?
There are a lot more idiomatic ways in English: Should I put ice in their glasses? Put ice in their glasses? etc. Again Translation theory used here needs to be meaning based as acceptable in the l 2
Is "nei loro bicchieri" ok?