Yes, it works just as solanthos wrote. You can only use one invader card one time for one campaign card, for another campaign you need another kill. The answer can be found here, it is FAQ number 15: http://www.draconisinvasion.com/faq
You can not find it in the rulebook, since this clarification came up only after the game was already printed. But that's why this FAQ section is for on the official webpage of Draconis.