well he kills james before jacob kisses bella and he loves her and he killed victoria because he loves bella no matter what he just wants her to be safe and happy!!!!
AOIFEB923 is right. Erdward loves Bella.
And he also wants her safe so it doesn't matter to him that she kissed Jake.
He would also want her safe if she choses Jakob over him.
Because he loves her. Whether she got tricked or not. He knows that Bella loves him more than she loves Jacob. He knows that if he had died in 1918 that she would be with Jacob, but he didn't and thats what matters.