That seems like an utterly bizarre claim. For a start, the US and Russia have not always been on poor terms. Russia did officially support the Union during the Civil War, though they did not lend military assistance (nor was that asked of them), for example. The sale of Alaska to the United States in 1867 is another notable instance of Russia getting on well enough with America to be willing to sell the US a large chunk of territory. Russia and America were a part of the eight-nation alliance that intervened in China during the Boxer Rebellion in 1900. Even earlier on, relations between the two countries were cordial:

The United States and Russia, though "distant" politically and geographically, maintained cordial relations after the former had gained independence from England. Both countries had clashed with England over neutrality and the freedom of the seas. The Treaty of Amity and Commerce with France (1778), the Treaty with Prussia (1785), and again the Treaty of Mortefontaine with France (1800) that the United States concluded included the principles of neutral rights. This was one of the reasons for the War of 1812 between the United States and England. For its part, Russia twice formed the League of Armed Neutrality with Denmark and Sweden, first in 1780 during the war for American independence and again in 1800 during the Napoleonic Wars. Although Russians later fought with the British against Napoleon, they continued to be suspicious of the British government which in turn considered that "only fear controls" the mind of Alexander. Half a century later, the United States and Russia signed an accord on neutral rights, two years before the 1856 Declaration of Paris, that was the first general international law on maritime rights.

From: "The Monroe Doctrine and Russia: American Views of Czar Alexander I and Their Influence upon Early Russian-American Relations" by Hiroo Nakajima.

There was economic rivalry between Russia and America in the northwest, especially prior to the sale of Alaska, but nothing that really threatened to cause war between the US and Russia. The sale of Alaska occurred because of strategic concerns - mainly, Russia saw Britain as their main strategic rival (this was during the "Great Game," the competition for influence in Asia between those two empires) and the US was a potential counterweight to that. Alaska in any case would have been hard to defend in case of war with Britain. In other words, strategic concerns outweighed economic ones.

Basically, Russia and America were on more or less good terms prior to the establishment of the Soviet Union. There was certainly no engrained dislike for America caused by Chesapeake Bay tobacco, and I can't even find any sources for that claim.