This question already has an answer here:
When Bran got his Three Eyed Raven Powers, it is reasonable to see Bran's company (Meera, Hodor, etc.) believe that he has these visions because they can actually see even the Children of the Forest.
But how did Tyrion and many others easily believe to what Bran says? Personally, I think it should take time to believe how someone with visions can see the past and present. Especially that Tyrion didn't even believe there were White Walkers until he saw one.