1. The men who signed the Declaration of Independence were not American citizens. They were British citizens. They were every much citizens of England as Americans today are citizens of the United States. They were simply British citizens living abroad, much as many Americans today live abroad.
2. Once the fighting started, British citizens, both here and at home, were exhorted to support the troops. It has been estimated that about 1/3 of the British citizens living here did support the troops and thanked them for their service. Another 1/3 stayed neutral. But the remaining one-third, including those who signed the Declaration, refused to support the troops. In fact, not only did they refuse to support the troops (and thank them for their service), they actually did their best to shoot them and kill them.