why can't it be yüzüyorken?
If you read the tips and notes on this section, there's no mention of using the continuous suffix. It only says to use the aorist suffix. It says to say "root-aorist-(y)ken". I don't know if you could use the continuous suffix here though.
It can be used if you really want to denote past continuous tense.
Does it make a difference if you say "Yagmur başladı çocuklar yüzerken"? It was marked wrong, but I don't understand why.