Most immigration in 00-10s was economical, and yes, for that group of people it's often the case that they are very much still enmeshed in Russian imperial agitprop. It's common enough that there are memes about this: https://lurkmore.media/%D0%9F%D0%BE%D1%80%D0%BE%D1%81%D1%91%...

However there was a smallish wave of political immigration after the 2011 protests and 2014 conflict with Ukraine, and a much larger one since the invasion of Ukraine in 2022. And those people tend to be very anti-Russian-government for obvious reasons.