In the United States in 1927, on the Petition for Naturalization (Form 2204-L), applicants would complete the line :
I emigrated from .... in ....
For example, here is a Petition FHL Film # 004112253 image 909 from the digital collection Pennsylvania, Eastern District petitions for naturalization, 1795-1931 / United States. District Court (Pennsylvania : Eastern District) at FamilySearch.
Was this the date of their last or first arrival to the United States, or was there no specific rule?
My guess would be that it was the date of last entry as naturalization required continuous residence in the States, but this is only a guess.
In the History of the Declaration of Intention (1795-1956) on the USCIS website, in the section about Form 2202 (Sept. 27, 1906-June 30, 1929), they only specify that what was required is the date and port of arrival. Again, no precision on whether this was the earliest or latest arrival.