According to Wikipedia:

A Tozama daimyo (????, Tozama daimyo?) was a daimyo who was considered an outsider by the rulers of Japan. The term came into use in the Kamakura period and continued until the end of the Edo period.

The daimyo who submitted to the Tokugawa shogunate after the Battle of Sekigahara were classified as tozama. Many of the largest fiefs were ruled by tozama. The biggest was the Maeda clan of Kaga with a value of 1,000,000 koku. Others included the Shimazu family of Satsuma, the Mori, the Date, Hachisuka, and the Uesugi. Many, but not all, of these families, had been living in roughly the same regions for centuries before the Tokugawa shogunate.

Tokugawa Ieyasu had treated the great tozama vassals amicably but later, between 1623 and 1626, Tokugawa Iemitsu was less tolerant of them. Particularly in western Japan, the tozama daimyo heavily profited from foreign trade in the mid 17th century. Their growing success was a threat to the shogunate, which responded by preventing the ports of western Japan and Kyūshū from trading.

To keep the tozama in check, the shogunate stationed fudai daimyo in strategic locations, including along major roads and near important cities. The shogunate ordinarily did not appoint tozama to high positions within the government. These went instead to the fudai daimyo.

Tozama daimyo from Satsuma and Choshu (Shimazu and Mori clans respectively) were responsible for the fall of the Tokugawa Shogunate during the Bakumatsu era. They were not loyal to the shogunate and saw the opportunity to seize power during this time. Shimazu and Mori both united behind the Emperor of Japan to renew and westernize Japan in the face of perceived Western dangers. Afterwards, the Shimazu and Mori clans had the most influence in the military and government of Japan until after World War II.


(Wikipedia contributors, “Tozama," accessed 3/16/08)

This reference appears on page 192.
Robinson uses this reference in the chapter when the Emperor’s senior generals were looking for a way to suit his wishes, so they proposed that the Emperor’s diplomats arrange a treaty with the Tozama Daimayo. The treaty was anticipated for order that the shogun would invite the Chinese to come to one of his ports and open it permanently to Chinese trade. This would cause the Chinese navy to be forced to land at this port, and would basically make the port a Chinese port which would then be secured by the full control of the Chinese navy.