Double negatives are not used in Esperanto:
Diru nenion al iu ajn!
Don't say anything to anyone!
However, if you use two negative words, the meaning changes:
Diru nenion al neniu!
Don't say nothing to anyone! (= Say at least something to everyone)
However these kinds of sentences are very uncommon, and I'd rather assume the speaker made a mistake and intended the first meaning.