No voter would or did.
Prior to 1804 each elector cast two votes for President. The person with the most votes became President. The person with the second most votes became Vice President. All 69 electors chose Washington as one of their votes on their ballots. It was more or less informally decided before the votes were even cast at Washington would be president. He remains the only president to be elected unanimously.
The ballots were split on the second slot, with Adams receiving a plurality of ballots. But every ballot that Adam's name was on, also had Washington's on it as well.
When John Adams and George Washington were considered in the first presidential election they were elected by the Electoral College. This body was the body created by Article II (and eventually amended by the 12th Amendment after Thomas Jefferson's election as Vice President) of the Constitution which describes the executive.
The direct answer to your question is that in many cases the "voters" (a.k.a "electors" appointed by each state's legislature) in the first presidential election voted for both George Washington and John Adams. Before the 12th Amendment the voters (a.k.a. electors) in the presidential elections cast two votes. (http://www.history.com/this-day-in-history/washington-unanimously-elected-by-electoral-college-to-first-and-second-terms)
The number 1 vote winner, if he won greater than half the total number of voters, would become president. The first runner up would become vice president. (http://www.270towin.com/1789_Election/) This system worked while the Federalists were popular. It wasn't until the first and second vote winners were from different political parties that the system needed to be changed for practical reasons. (http://www.usconstitution.net/xconst_A2Sec1.html)
Given that Washington was elected unanimously (meaning every elector cast 1 of their ballots for him) and Adams was obviously not elected unanimously (he did not win the presidency against Washington) there were some electors who voted for Washington and another candidate instead of voting for Washington and Adams. The real question that should be asked is: what kind of elector would have chosen a different second choice candidate over John Adams? (this could highlight potential North/South divisions or Federalist-Anti-Federalist/Democratic Republican divisions.
According to Federal Archives: http://www.archives.gov/federal-register/electoral-college/scores.html
The 1789 Electoral College election results broke down as follows:
George Washington (69) Total Number of voters (aka electors) = 69 John Adams (34)
The others: John Jay (9), F Robert H. Harrison (6), F John Rutledge (6), F John Hancock (4), F George Clinton (3), DR Samuel Huntington (2), F John Milton (2), From GA James Armstrong (1), Benjamin Lincoln (1), F Edward Telfair (1) From GA (Total 35)