No, think of the map in the video. Say there are 10 bases to attack. Thats a max of 30 stars for the war. If you attack base 1 for one star and another one of your players attacks the same guy for 1 star it's only one star towards the war total and will only appear as one star on the map. The stars increase if you two or three star them, they don't stack or accumulate.

