The words were written by Perfyonov. (that’s for sure).
Aturov just brougt the song to Alexandrov in 1929. Songs to this meloty were written from 1914 to 1919 in different places of Russia (Moscow, Siberya and Ukraina). It is illogical that Aturov composed it, tough there is no evidence to such a sonf before 1914.