After the break up of the soviet union, Russia with a help of Koloskov was named a successor of the soviet soccer. While Ukraine couldn't particepate in any offical competions, Russia had a chance to go to the 94 world cup. They took most of our best players such as Onopko, Uran, Nikiforov, Kancheleskis and Cimbalar'. Some others like Litovchenko, Protasov and Michalechenko declined the offer. Other Ukrainians that now are playing for Russia are Semak and Karyka.
Some of the players in question, like Onopko were also playing for Russian clubs at the time, so there was a lot of pressure on him to play for Russia. That would affect the decision one makes.
Second, the CIS team that played in the EURO92 was composed mostly of Ukrainian and Russian players, and it was a decent team, who many thought would do well in the WC, so some players may have acted in the best interest of the team, preferring not to break it up.
Third, and someone who's Russian or Ukrainian(more than me, anyway ) will have to help me out, some of these players may have had Russian roots. If I recall correctly, every former Soviet republic had a Russian population that accounted for at least 5% of the total in 1991. It wasn't all that uncommon for people to move from one republic to another. Danilevicius, the Lithuanian striker known better for his fake passport than football skills was born in Mocsow. Kanchelskis' last name sounds Latvian. Many players playing for Kazakhstan are ethnic Russians. Once again, someone else can probably help out here.
There are quite a few players who played for Russia despite being born in other republics, here's a quick rundown of some of them:
Karpin - Estonia
Tsveiba - Georgia
Tetradze - Georgia
Rachimov - Tajikistan
Mukhamadiev - Tajikistan
Dobrovolskiy - Moldova
You have to remember that Russia were able to convince Fifa to make them the succesor of the soviet union soccer. Ukraine disagreed and suggested that they atleast play a game to determine who should be a succesor. Russia declined. As for the player's roots I am not sure, but all of them were born in Ukraine. Also historicaly Ukraine and Russia had a huge rivary between them, Dynamo Kiev and Spartak were the worst enemies, that's why Ukrainian fans were very angry with both the players and Russian officals. It was a huge blow for Ukrainian soccer which stoped its development for some years.