Hokori Otaku 
Okay, here’s a working theory on why I think Koji might have known that once he mentioned Yodo could have been saved, Boruto would jump onto the battlefield and go against Jura.
Firstly, let’s look at the way Koji reacted to Boruto entering the battlefield. We can compare his reaction when he was in the Ten Tails’ realm with his reaction when Boruto went up against Jura.
When talking to Eida, he seemed relatively calm. However, when he was in the Ten Tails’ realm, he got a bit upset; or rather aggressive; trying to tell Boruto to get out of there. But here, he just calmly announced that Boruto was done for.
Koji is the kind of person who can make sacrifices if it means the mission will be completed or the right results will come from those sacrifices. A good example is Yodo, or in the past, how he kept lying to Jigen even though he knew he could get caught at any time. For the sake of the mission, he can go to any length.
To do that, though, since he has been working with Boruto, he doesn’t completely reveal everything at once. Instead, he feeds everyone the right information at the right time. Even with his expressions, he seems well in control of what he wants to show; and so far, that has worked in his favor, as he appears to remain in control in the current arc.
Now here’s a little stretch from my side. It’s fair to say Jura is more powerful than the current Boruto. Boruto doesn’t stand much of a chance against him. So far, Kawaki is getting his power-up, Sarada got hers, but Boruto has only leveled up his skills. Now could be the chance for him to finally get his power-up.
Remember the situation when Kawaki pierced Boruto? When Boruto revived, he said he felt more in control of that power, although it didn’t last long before Momoshiki took over. Still, we can say Boruto getting into life-or-death situations might bring him closer to his Karma powers; or maybe allow him to gain control like Kawaki does.
But for that to happen, Boruto might have needed to go up against Jura. That could be the only way for Boruto to get a power-up. I’m going to say the Jōgan. Koji might have seen in one timeline that Boruto had a reaction to a near-death situation, and that this flow of actions is what triggers it.
This might be a stretch, but I feel like it’s something that’s possible.