Nothing is contradictory here. When Madara wanted to talk about his sharingan, he stopped and did not complete his answer. Clearly Hahsirama did not catch the leak. Therefore, to Hashirama, Madara unlocked his sharingan in the action of 624. From Madara's family standpoint, it is clear that they never saw Madara with Sharingan. This is very plain in the chapter given Izuna's words and their father's comments. So if we want to see logic in the sequence of chapters, it is easy to see that Kishi did not screw anything.
Another interpretation is that Hashirama might not have meant that Madara just unlocked the Sharingan (because he never said that Madara just awakened it). Rather,. Hashirama saw that Madara has already awaken the sharingan, and took not of it. Thus, again, there is no contradiction.
My opinion is that some people are so disappointed about the revelations Hashirama is giving about Madara, that they want Kishi to be wrong.
Let analyze Edo Madara for example, since he was revived:
1. He used only Susanoo as a signature Uchiha jutsu. He also used genjutsu on a weakened raikage. Then as Uchiha, he used fire jutsu. Apart from that, we saw Perfect Susanoo whose origin is has not been decided across the forum.
2. Madara has used Hashirama's Jutsu in each one of his final or decisive blow. Madara has been spamming Rinnegan, thanks to Hashirama's DNA and the fusion that Kabuto did.
3. As soon as Madara shown up, the first thing he tried was to summon Kyuubi.
All these show that though Madara was a badass for regular shinobi clan, he does not really show all the hypes about him when it comes to facing his natural rival - Hashirama.
Besides, according to history, the greatest account on Madara is about taming the Kyuubi - which is nothing but having a super genjutsu. My opinion is that Madara's fan should pray that Hashirama did not let him live, because it would be a disgrace to him. In fact, one of my opinion is that Madara became a legend because every time he came back alive from a battle with Hashirama, his contemporary did not know that he was spared. Rather, they thought he survived because Hashirama couldn't kill him.