Of course they used demintives - Alyosha, Mashka, Nastya, Olenka, as your nickname is also one deminutive -- Sarushka. ; )
If you can prove that, I'd be delighted. The only nicknames I've occasionally seen in writing are: Olenka, Tatianochka, Mashka, Masha, Nastya, Nastaska, Nastasya, and Schvybzik/Schvybs. Never Olya, Olishka, Tanya, or Alyosha, as livadia.org claims.
(We should probably start a new thread for this question.)