Identifying people who admire Putin as Putinistas should not be an insult. They treat him with awe and reverence, like Christ. They claim his grievances are legitimate and his will to power makes sense. He has been wronged by Soros, the Rothchilds, World Jewry, and the nefarious and ever present sneaky neo-cons, no less. They see a strong man on a horse, a scuba diver, a bare-chested wrestler of wild animals, and they become gushy with feminine cooing, enthusiasm that is normally seen by little girls at a Justin Bieber concert. Just as there were Americans who hated Roosevelt so much that they were Hitlerites until he declared war on the USA, there are those who are Putinistas. Admittedly, Obama is a jerk and a threat to American liberty; he's liable to bankrupt us. Yet why two wrong-headed statist leaders make a right (pun intended) is beyond my ken.
As for what Putin thinks, this link, I believe hits on it pretty well and explains some of the possibilities to concern ourselves with. http://www.washingtonpost.com/blogs/monkey-cage/wp/2014/03/02/how-putins-worldview-may-be-shaping-his-response-in-crimea/