Lin Fan only stayed another day in the Alchemy King Hall after the contest.
After all, there was nothing else left for him to do there and he had already wasted enough time in the Alchemy King Hall.
There were other things that he had to do, but he had taken time out of his schedule to come here because of Song Shu.
Song Shu had wanted to go with Lin Fan, but knowing that this was a delicate time, the Alchemy Master didn't allow this.
In just a single day, he had already gathered more than enough information to get a general idea of the situation. He knew that the Thunder Sect, the True Spirit Sect, and the Assassins Association would certainly be watching Lin Fan's store and if he were to allow Song Shu to go with Lin Fan, wouldn't that be declaring that their Alchemy King Hall was on Lin Fan's side?
Before everything had been settled, he wasn't willing to let this happen, so he wouldn't let Song Shu go.