I've already read this faq http://www.reddit.com/r/AskHistorians/comments/2aueh6/how_did_the_russian_empire_manage_its_nonrussian/ and some others but what i'm interested in is if the people living there rebelled against the russian rule and feel them as foreign like i believe polish did or if they liked to be ruled by people closer culturally and religiously.
I only know the perspective of the Russian revolutions in the early 20th century, but in those the issue of subnationalities within the Russian Empire was pretty huge. Before the 1905 revolution the tsardom had effectively banned languages like Georgian from education and administration. But during the revolution there was a momentary crisis in the authority of the tsar and the subnationalities flexed their cultural muscles and pondered independence along either communist or nationalist lines. A fulcrum point that both anti-tsar socialists and parliamentarians would use to advocate for regime change in St. Petersburg was by flexing regional power and identity. When imperial power was reasserted the subnations entered back into the realm with a little more bargaining power, if only because in that period and out of political expediency a national identity had been fashioned.
Prior to 1905 the Ukrainians were called 'Little Russians,' opposed to the Muscovite 'Greater Russians.' Moreover, the central uniting factor amongst people prior to the imperial age was religion: in this case the Russians (by which I mean greater and little) were united by the Orthodoxy.
My point is that the subnations living within Russia were more or less constructed in response to the politics of the Russian empire. Rather than understanding these groups as existing forever before the empire and reacting to the empire as a coherent people, identities are formed over time in reaction to meaningful distinctions in politics.
However, I think there's a lot to say about the Turkish groups like the Tartars and the Turkmens. Stalin himself served as Commissar of Nationalities in the early days of the Bolshevik regime (partly due to his transition from Georgia to St. Petersburg) and reading about his own efforts to define nations and figure out what to do with them is illuminating to the whole complicated deal.
How complicated? The 1897 census recorded 104 nationalities speaking 146 different languages. Each nationality's perception of the Russian empire and whether the Tsar represented them was internal to the constantly flux thing called nationality. It's a violent history with either genocide or quiet abdication depending on who you're talking about.
Source: Kotkin, Stephen. Stalin Vol. 1: Paradoxes of Power. 2014.
Also relevant: Anderson, Benedict. Imagined Communities.