After Alister became a 10th-Circle Mage, he didn't dive into the Sea Of Chaos yet. The chaos-attributed mana that was radiated by the Sea Of Chaos wasn't enough to create Alister's ultimate magic circle.
From the first to the tenth magic circle, they were all engraved inside the mana core. However, when a 10th-Circle Mage attempted to become a Master Mage, creating the ultimate magic circle was needed.
The ultimate magic circle was a higher version of the usual magic circle. Instead of being engraved inside the mana core, it was engraved outside and on the mana core.
For a more crude explanation, the ultimate magic circle was like a sticker that would be plastered on the mana core. Having an ultimate magic circle would make even a 1st-Circle magic spell a lot stronger than usual.