This episode is largely regarded as the "Spock's Brain" of the animated series. No reason is given as to why the crew de-age so quickly. They were only in the negative universe a few days at most. While they would de-age, it would not even be noticeable. They certainly would not have become children.
In Karla Five's first message to the Enterprise, she's speaking in reverse. Later, in her reverse-time universe, the crew can understand her (and her, them) because, as Spock says, their brains are now in reverse. If this true, then Karla's brain should likewise have been reversed when she entered the forward-time universe, allowing her to speak forwards.
The entire crew of the Enterprise becomes younger at an alarming rate, even Mr. Spock who says he ages the slowest. However, Commodore April and his wife cease to become younger after he's taken command. They too should have become children by the time the ship was out of danger.