We know that the timer went off several seconds before Marty floored the accelerator. We know that Marty quite literally hooked the line at precisely the correct time. Therefore the only valid conclusion is that Marty accelerated faster than Doc calculated/anticipated/intended.
Thus there are only two valid explanations:
(1) Doc planned for Marty to accelerate at a rate less than the car's maximum acceleration. This leads to the obvious question: How would Marty know how fast to accelerate? We can suppose that he did some test runs off screen, or we can attribute it to movie magic ("he eyeballed it!").
(2) Doc miscalculated the maximum acceleration of the car. Although a genius, perhaps there were aspects of the car that he had no way of determining in advance. Or maybe there was less fuel in the tank (less mass to push) or better road traction than he anticipated (although the roads seemed pretty slick, IMO). Either way, if he did make a mistake and the timer was set to assume maximum acceleration, then Marty was very lucky.
There is a third option (Marty was always supposed to wait X number of seconds after the timer went off), but that isn't directly supported by anything canonical in the movie.
The flexibility of the hooking mechanism or any other such variance in exactly when Marty hit the cable is negligible. He clearly left the starting line many seconds late. Any question about whether the flexibility of the hooking mechanism impacted his arrival time would only have an impact on the order of milliseconds and may thus be discounted for the purpose of this question.
The speed of the lightning through the cable is obviously shown to be quite slow for visual impact in the movie. Obviously in real life it would have traveled faster than that. In any event, Doc would have been able to calculate the speed of the lightning through the conductor, so let's assume he was accurate there.
Unfortunately any discussion surround whether the lighting struck at "precisely" 10:04:00 or sometime between 10:04:01 and 10:04:59 is a red herring. The fact is that the movie depicts the lightning as striking immediately after the minute hand moves to 10:04. It's not made clear in the movie how 1955 Doc knows that it will be "precisely" 10:04:00. (My guess: clock engineers in the intervening years investigated the clock, observed that it was "precisely" 10:04:00, and then documented that fact in the flyer that Marty received. But exactly how that information came to Doc is beyond the scope of the question the OP asked.) Regardless, 1955 Doc is correct -- lightning did strike at precisely that time.