Thank you, jf42. The information that you provided is very helpful. One of the universities local to me has a copy of the Katcher book, so I will examine it soon.
i know that the 57th Regiment of Foot was on New York Island on 31 July 1783 because a muster roll was signed at that location on that date. Most muster rolls that I have searched for that regiment cover six-month periods from 25 Dec to 24 Jun and 25 Jun to 24 Dec. But the period around the evacuation of New York was probably not business as usual. The next muster roll after the 31 July 1783 one was signed at Annapolis Royal, Nova Scotia, on 11 Oct 1784. This is the muster where my ancestor is shown as enlisting on 25 Aug 1783, so this muster covers more than one year.
I agree that muster rolls usually show where a soldier was transferred from or to. I looked at the muster rolls for the 57th up to 1786 and most do show that information. But in the muster roll covering August 1783 to October 1784 (over 14 months), no information is given for any officer or soldier about transfer to or from another unit. The only designations next to some names (along with the date) are "enlisted", "discharged", "died", and "deserted". My hypothesis is that, for this one muster roll, they lost track of some of the information about other units so they did not record it.
As to whether my ancestor enlisted on New York Island on 25 Aug 1783 or if he enlisted in Britain: (1) the regiment was still on New York Island on that date because the book History of the Fifty-Seventh (West Midlands) Regiment of Foot (1755-1881) by H.H. Woollright (1893) says that the regiment only transferred to Nova Scotia in Oct 1783, and (2) my ancestor wrote on a land grant application that he served during the American Revolutionary War (a claim that would not be true if he enlisted in Britain and joined the regiment in Nova Scotia).
Woollright also says that orders were issued in June 1783 to reduce the regiment from ten to eight companies. As a result 10 drummers and 67 privates were discharged in August 1783 and provided passage with their wives and children. That is why I don't think that new men were being recruited on New York Island on 25 Aug 1783. My theory is that there may have been some shuffling between regiments to accommodate those who wanted to stay with a regiment in Nova Scotia and those who wanted to be discharged to Britain. In addition to many men shown as discharged on 25 Aug, there were also very many shown as enlisted on that same day.