First of all, there is no single Chinese language. People from China and their descendants speak a variety of languages belonging to the Sinitic family, sometimes several within one house, sometimes different between generations. Sinitic-speaking people also do not necessarily come from China: they may also hail from Taiwan or Singapore, and Hong Kong and Macau were only recently incorporated into the PRC. There are also significant Overseas Chinese ("Chinese" here meaning ethnic Han) communities all over Southeast Asia, most notably in Malaysia, but also Indonesia, Myanmar and elsewhere.

Spellings such as Liu, Zhang, Xie follow the rules of Hanyu Pinyin, the Mandarin romanization convention promoted by the PRC, and used in many places around the world nowadays. Before its existence, there were other romanization schemes, for example Wade-Giles, but those weren't as well-known or as widely used, and in many cases people's names were written in an approximation of English sounds, e.g. 李 (pinyin Li) being written as Lee, due to it also being an English word (and surname!).

The above was just for Mandarin. There are also plenty of Cantonese, Hokkien, Teochew, Hakka, and other speakers living outside of China, and they may choose to use their native language's pronunciation in the romanization of their name instead of Mandarin. This can give names like Wong, Ng, Tan, etc.

Note that the reverse is also possible: for example the surname 李 in Korean is pronounced [i] (like English "ee"), but Koreans still spell it as Lee, for example Lee Myung-bak. Bruce Lee's family name is the same character, but it's actually pronounced [lei] in Cantonese, which he spoke.

On top of all this, before the proliferation of Hanyu Pinyin in China, there was no systematic way to romanize names that people commonly knew. This is true to this day in Taiwan, which does not use Pinyin in education, and so names can and are spelled differently, using Wade-Giles, Pinyin, or any other convention, including one of the person's own make.

So the tl;dr of this is no, you generally would be hard-pressed to pinpoint the time a Chinese American family immigrated. The unambiguous use of Hanyu Pinyin in the name can be a hint that they came after its proliferation in China and elsewhere, so in the last 50 years, assuming that they haven't changed the spelling of their name since. Using a different spelling convention would not necessarily imply an earlier time of immigration, since the family could come from somewhere other than the PRC.

Edit: Also, paging /u/keyilan in case he wants to add something or make corrections to my post.