Yes, 'like adults' and 'as adults' have completely different meanings. Remember that 'like' means 'similar to'. A crocodile is like an alligator, a clementine is like an orange. These things are not the same, but they are similar. So, for example, you would say: "Those kids are very clever. They're only 11 years old, but they talk like adults." In this case the people aren't adults - they're only 11 - but they talk in a similar way to adults. In your sentence, the only correct word is 'as'. The phrase 'as adults' means 'when they eventually become adults'. In this case we are talking about the people really being adults i.e. actual adults, not kids who are similar to adults.

In this case, only "as" is correct because it refers to the capacity of a person or a thing - here "an adult". e.g. I work as a teacher. I will use the table as a seat because there are no chairs in the room.