Here is what the Alien Enemies act says in the first section... It isn't just people we declare war on.... there is an "or" in there for a reason.
An Act Respecting Alien Enemies
SECTION 1. Be it enacted by the Senate and House of Representatives of the United States of America in Congress assembled, That whenever there shall be a declared war between the United States and any foreign nation or government, or any invasion or predatory incursion shall be perpetrated, attempted, or threatened against the territory of the United States, by any foreign nation or government, and the President of the United States shall make public proclamation of the event, all natives, citizens, denizens, or subjects of the hostile nation or government, being males of the age of fourteen years and upwards, who shall be within the United States, and not actually naturalized, shall be liable to be apprehended, restrained, secured and removed, as alien enemies. And the President of the United States shall be, and he is hereby authorized, in any event, as aforesaid, by his proclamation thereof, or other public act, to direct the conduct to be observed, on the part of the United States, towards the aliens who shall become liable, as aforesaid; the manner and degree of the restraint to which they shall be subject, and in what cases, and upon what security their residence shall be permitted, and to provide for the removal of those, who, not being permitted to reside within the United States, shall refuse or neglect to depart therefrom; and to establish any other regulations which shall be found necessary in the premises and for the public safety: