Putin wants to keep Russia one country, rather than see it break up into several. If Muslim territories succeed in gaining independence, other areas will demand the same. So he will try to consolidate power in the central government.
Russia is too weak militarily and politically to defeat these Muslim rebels any time soon. The Russians will be tied down for many years just trying to maintain the current borders of the country. A revival of the former USSR in terms of expanding territory is not an option.
Does this mean that the Russian government will become as brutal as the former Soviet Union? That is certainly a possibility. Hopefully Putin will put more resources into building a better economy than copying the former police state.