The first state reacted before the fall of the Ming; Joseon saw the writing on the wall after the Manchu invasion of Korea and started sending tribute to the Qing instead of the Ming. The Japanese were highly isolationist at the time, so they didn't offer tribute to the Qing, but not out of any preference for the Ming, who'd kicked them out of Korea a half century ago. Burma, which became the shelter of a pretender to the Ming throne, was invaded and plundered by Wu Sangui's troops, and the dynasty entered a period of decline. Generally, though, most states that paid tribute to the Ming for trading rights continued to do so for the Qing after they'd made it clear the Shun and Ming weren't coming back.

In the Netherlands, or at least in the offices of the Dutch East India company, it was seen as an opportunity. They had tried, for years, to open trade relations with China, but never really succeeded. Both violence and diplomacy failed. They had been allowed to set up shop on Taiwan (not yet part of the empire), and Chinese traders were allowed to go there, but that wasn't really the same as direct access to Chinese products, like the Portuguese had in Macau.

After the Ming fell there was hope that their successors, would be more open to trade. In the end, they were disappointed. Despite Dutch ambassadors making it as far as the Chinese court, and even some joint military actions against their common enemy the successors of the Ming loyalist Koxinga*, there was no regular trade with China until the 18th century.

*He had kicked the Dutch out of Taiwan in 1662.