The end of 1907 is also the time when the 'Immigration Act of 1907' was passed, one of the first major legislation that in fact 'regulated' immigration and codified 'requirements for entering the US.' According to the act, notable number of immigrants who are deemed 'diseased and disabled' are barred from entering. To enforce this, medical examination and a codified set of interview questions were established.
But this act also caused other reasons to barr immigrants. If an immigrant cannot answer the question, or answer it in an unacceptable way, they are automatically barred and forced back without further conversation. For example, if a women cannot tell how she will gain an income in the US, who she will live with, etc., then she can be barred from entering under the pretense of 'potential prostitute.' Asian immigrants were further scrutinize as now they must understand english to answer the questions.
So, this is why the numbers halved so suddenly in 1908.