This is a good question and I'm a bit surprised Toll doesn't break that down (I checked my copy and you're right about that; weird). I actually don't know how that number is associated with the original cost, because of reasons I'll explain below, but the actual cost of the six frigates exceeded that.

Wikipedia, being ever unreliable, ties that figure to the Naval Act of 1794, but you can read the act itself on the wiki page, or in a printed version here, and in doing so you'll notice that the Act does spell out rates of pay, rations, roles/manning and complement of crews, but does not list that cost amount anywhere on the page.

The Act was preceded by Congress voting to form a committee headed by the Secretary of War to study the ship types needed by the navy, and the Act itself provides for either building or purchase of four 44-gun ships and two 36-gun ships.

At the time, the seat of the government was in Philadelphia, which also happened to be the largest port in North America, so Secretary of War Henry Knox consulted with several people, including naval architects Joshua Humphreys, shipbuilders Josiah Fox (more on him later) and James Hackett, and also John Barry and John Foster Williams, who had been captains in the Revolutionary War. Unfortunately, these meetings were held in person and minutes weren't taken or haven't survived, so we don't know exactly how this was discussed, but the group decided on building ships from scratch rather than procuring them elsewhere. That is probably the point at which they estimated the 688,888 figure, but I can't offhand find where the actual appropriation is.

We do know that Humphreys was appointed the main designer for the ships, but he and Fox fell out over the designs and Fox actually drafted the plans to a smaller scale, which led to him being demoted.

The way the ships that were designed by Humphreys were actually built was that the Navy awarded contracts to people at six different shipyards, in six states -- as a contractor yourself, you may be familiar with this type of procurement logic. Each shipbuilding site had a naval constructor and superintendent, and although plans for the ships had been drafted by Humphreys and his team (minus Fox), each constructor had fairly broad leeway to interpret the plans. Fox was actually appointed constructor of Chesapeake in Gosport (Humphreys was constructor of United States in Philadelphia), and Fox wound up building Chesapeake to be shorter, broader and to carry fewer guns than its specifications -- it wound up being considered its own "class" inasmuch as there were classes then, and was rated for only 36 guns, though it had been designed for 44. (I wrote about its capture by HMS Shannon captained by Philip Broke in an earlier thread.)

The construction of the frigates was not a well-coordinated task. One of the clauses of the Act of 1794 was to suspend construction on three frigates if there was a peace with Algiers, which happened in 1796 -- at this point, the three ships nearest completion (United States, Constellation and Constitution) would continue construction, while building on the others was suspended until the Quasi-War with France happened and Congress agreed to continue building them. In any case, in 1797 Congress was forced to pass further appropriations to build the first three frigates -- $372,000 in two separate appropriations; and in 1798 another $600,000 for the last three frigates, the last of which (President) did not launch until 1800.