Tsar Alexander I provided military muscle for the Holy Alliance, a group of despots determined to keep nationalists and liberals down after the fall of Napoleon. The USSR had the Brezhnev Doctrine, by which it claimed to have the right to keep Warsaw Pact countries as, effectively, socialist colonies. Is it then any surprise that Vladimir Putin is asserting his right to intervene to keep authoritarians in former USSR republics in power?
Of course not. The real question is which of the historical analogies is more appropriate. Putin’s autocracy looks more like the Russian Empire than the USSR to me, so I would say that he more closely resembles the Tsar.
To be fair, you could also say he looks like Theodore Roosevelt. The Putin Doctrine and the Monroe Doctrine aren’t all that different.