Time travel in The Philadelphia Experiment (1984) is kept simple, there is no "new" timeline created. Jim Parker goes forward and then back in time and David Herdeg is remembered by other crewmates as the one who stopped the machine.
But it's more complicated for The Philadelphia Experiment II (1993). The way I understand it, there was a alternative timeline created when the Phoenix was sent back in time and destroyed Washington. David Herdeg remembers the "old" timeline because he was part of the experiment and came from the same time breach, or something like this.
But I lost all my bearings in the end. When Mahler (the father) is killed, it causes Mailer (the son) to disappear. Wouldn't the destruction of the Phoenix supposedly cause the disappearing of Mailer right away since he didn't had any reason to time-travel to 1943 if the Phoenix was destroyed? If it's because he came from a different timeline, why does he disappear when his father is killed?