Dinah was from Earth II which was 2 decades behind earth one and still fighting Hitler in Earth One's 1970s.
Earth X was the Earth that was fighting still WW2 in the 70's (the Nazi's won WW2, but there was still a fighting resistance). It was the pre-crisis home of the Freedom Fighters, and although apparently at one point it was retconned (probably pre-crisis) so that the Freedom fighters migraited from Earth 2 to Earth X (according to wikipedia), the JSA was never there and never fought there.
The JSA stories in the 70s All Star Comics run and later Infinity Inc definately took place in real time (aka the 70s, 80s, etc). I've read the whole All Star Comics run and a lot of Infinity Inc, and they all agreed that the JSA fought in WW2, which ended when WW2 actually ended, and that they all existed without looking much older in the 70s and 80s.