I read recently that the hot peppers characteristic of Sichuan cuisine likely came from Mexico and realized that I had never heard any other examples of New World crops reaching Asia. How quickly did settlers decide to exchange these new resources with nations such as China? Was it immediate, or did it take a while for things such as corn, tomatoes, pumpkins to be introduced?
Furthermore, was the impact felt? Would the average Chinese person know about brand new foods being introduced to their region?
Quite significantly. Manila had just started becoming a major trading port and many goods made their way through Manila on their way not only to Europe but also to China. For instance, the sweet potato plant was imported into Fujian province during a local famine, such that even today sweet potato greens are a relatively common vegetable dish in Chinese cuisine.
By far the biggest and most powerful import into East Asia from the Americas, however, was silver. Tonnes and tonnes of silver, freshly minted by the Spanish government at times, poured into Chinese trading ports as the Chinese economy hungered for silver to help expand the liquidity of the otherwise monetarily constrained Chinese economy. This was later supplemented by silver mines in Japan which also shipped silver to China in exchange for Chinese goods: however the strength and influence of the Spanish peso (or "piece of eight") was such that even as recently as the mid-20th century, Chinese currency was often referred to-and in some cases actively used-as the Mexican dollar.
While certainly the impact would be localized (as China was a very large country and outside of certain trading areas it was difficult for foreigners to penetrate deeply into China) some groups more than others were exposed to the European trade. Most notably, the areas of Fujian and Guangdong (in the ports of Amoy and Macau, for example) were the most exposed to foreign trade. Many Chinese merchants would also sail down to Manila and other trading ports in Southeast Asia (for instance, Malacca in Malaysia, and Batavia in what is now Indonesia) to establish trading posts that would deal with the Europeans and other traders bringing goods.
Of course, it is important to differentiate between products that were brought over during the Columbian exchange (and early modern times) versus those like the tomato (or in Mandarin, "foreign eggplant") which were introduced more recently towards the end of the Qing Dynasty and the Republican era. But that is another question which I unfortunately am less familiar with and cannot answer.