I understand that this response might be in violation of some of the rules of this subreddit, but I see no other way of addressing this question.
There were (and still are) indeed some groups that propagated Siberian nationalism and an independent Siberia (or at least an autonomous one). The peak of their development, however, was in the mid-to-late 19th century, when they enjoyed the support of some of members of Russian intelligentsia who were exiled to Siberia.
However, in modern times there really hasn't been any serious movements propagating Siberian separatism, and certainly never anything even remotely resembling an armed insurgency.
The most relevant recent (so recent, in fact, that it is in violation of the rules of this subreddit regarding the discussion of current events) example is probably that of "Siberian Wikipedia", a truly bizarre stunt wherein a Russian entrepreneur from Tomsk attempted to create a section Wikipedia in an artificial "Siberian" language. The crux of the matter was that the language was just a peculiar version of Russian, and certainly not a separate (or, indeed, real) language. It was eventually taken down, but while it was up a lot of the materials there propagated anti-Russian views and called for the creation of an independent Siberian state.
In general though such views are not (and, historically, were not) popular among the populations of the region. Think of Siberian nationalism as a slightly more absurd Russian version of an independent California movement.
Short answer: not that I know of, but I know less about Siberia than I do about the Caucasus.
Long answer: I haven't seen the film, but given the year it came out (1995), this line of dialogue could have been the screenwriters' attempt at an inoffensive reference to the general idea of post-Soviet separatist struggles. A bunch of satellites in the Caucasus and Central Asia declared independence in the early 90s after the USSR's collapse. Most relevantly, in 1995 Russia was embroiled in the first Chechen war. That was a separatist struggle, with Chechnya trying to gain independence after being conquered and held by Russia since its Tsarist period. However, Chechnya is in the North Caucasus (south-western Russia), not Siberia... but I'm not sure I trust your average Hollywood screenwriter to quite know or care about that geographical difference.
A bit more on the first Chechen war [is here] (http://www.globalsecurity.org/military/world/war/chechnya1.htm). A lot more could be said about that larger conflict; unfortunately, that would violate the 20-year rule, as unrest in Chechnya is still very much ongoing today.