The Revenue Act of 1862 imposed income tax withholding. According to
http://quod.lib.umich.edu/l/lincoln2/5250244.0001.001/1:17.4?rgn=div2;view=fulltext,
"Income tax was first collected under the general revenue act, approved July 1, 1862. A tax was imposed upon the salaries of federal officials at the rate of three per cent on incomes in excess of $600, and the disbursing officers were required to withhold the "income duty," as it was called, at the time of the payment of the salary.
"Some time was required to set up the machinery of collection, with the result that the
first withdrawal of $61 from Lincoln's salary warrant was not made until September, 1862. Thereafter his warrant was reduced from $2,083.33 to $2,022.33 a month."
Although I can't find a specific source
, presumably
Lincoln's salary for September would have been paid at the beginning of October, standard accounting practice
. I note that the question says "
in October" and not "
for October."
Another source: "According to the leading scholar of Lincoln's personal finances, the president was paying $61 monthly, or 3 percent of his $25,000 salary, minus a $600 exemption. These payments, moreover, were being directly withheld from Lincoln's pay in the manner prescribed by the 1862 revenue act." This source does not state when the withholding became effective.
http://www.taxhistory.org/www/features.nsf/Articles/27B1BC08AC974BBD85257BAA00436F8B?OpenDocument