So the thing is Julius' precog via manazone, at the minimum function differenty from Luicus' foresight which actually shows other worlds and timelines.
The thing is all mages read (feel) the flow of mana in their mana mana zones and react to it. It was stated that mana is invisible, mages can't visually see it, they only feel it/sense it.
Mana zone allows you to have top detection since you're controlling the mana around you. Yami's Iai slash condenses the mana zone and alerts him when the mana zone barrier is crossed. Using ki, Yami can predict when that barrier is crossed.
Julius mana zone is nearly similar since he can use his zone anticipate attacks by accelerating/aging the mana around him and reading(not visually)/feeling the aged mana to sense precise the disturbances that would happen, just like Yami does uses ki to anticipate future disturbances. In fact Yami compared his mana zone technique to Julius' function wise. So it's less that Julius is looking into the future, but moreso bringing the future to himself. Lucius's ability to foresee the future however appears to be different from the mana zone technique since you're actually looking into the future , rather than just aging the mana around you.
So in short, Julius uses time acceleration to fast forward the flow of mana in his manazone. He then reads (feels) that fast forwarded flow before the opponent even makes the attack. So it's like the mana skips ahead in real time or ages in real time. He's not actually looking ahead to the future in real-time but moreso bringing the future to him in real time. By sensing the changes in the glow of mana, while Lucius is actually looking towards the future, and seeing it with his eyes.