Actually, Tobirama's attitude was only natural in that situation. He has a very practical view of things. Furthermore, because of that practicality, he looks like a jerk when paired with Hashirama because of Hashirama's idealistic nature.
Can you really blame him for not trusting the Uchiha? Besides, he wasn't dissing Madara or anything, he was just pointing out to Hashirama what the people thought. Tobirama wasn't wrong when he said Hashirama deserved to be Hokage. He also wasn't wrong when he said that it was Hashirama who brought everything together. Madara just didn't like it.
I believe the reason for Madara's change of heart is not because of Tobirama, it's because he knew that his power comes from hatred. He wanted power to protect the Uchiha. But little did he know that Tobirama won't even actually hurt the Uchiha.