I have encountered such a problem. I have started a new corporation, and applied for faction warfare with it.
I am already in faction warfare, I can see for example my enemies displayed as enemies in faction warfare, but I cannot take over the structures in the sites meant for faction warfare.
The timer will not work, it still shows that the site is contested, but not counting timer.
I am enlisted with my new corporation in Caldari faction warfare, and is true I did jump only inside Caldari sites, but still as far as I know, the timer should work.
Can the problem be that my newbie corp is not eligible for war? But in that case if I cannot take structures in sites designed for faction warfare, is kind of lame.
I am new player, so maybe I do not know and do not understand the mechanics behind it.
Thank you for your answers.