As the token is created, it checks the printed values of the Giant Adephage it's copying—or, if the Giant Adephage whose ability triggered was itself a token, the original characteristics of that token as stated by the effect that put it onto the battlefield—as well as any copy effects that have been applied to it. It won't copy counters on the Giant Adephage, nor will it copy other effects that have changed Giant Adephage's power, toughness, types, color, or so on. Normally, this means the token will simply be a Giant Adephage. But if any copy effects have affected that Giant Adephage, they're taken into account.