There perhaps is one valid reason for them to: Minorities can get big preference by being extremelly loyal. Majority can't because there is only one pie.
The fed money transfers from Moscow to Caucasus and nat. republics are huge, and that's their deal: Moscow pays, the republics' rulers provide near 100% votes.
Chechnya usually votes close to 100% for Putin, simply because a lot of government money is poured in Chechnya, disproportionately more than in any other region of Russia,