After spending this time in the core area you can say Alex is getting both because He did not find any clue about the demons so he began to think most likely this is the time to go back. But as you know the city Lord gave him mission to stay inside the core area for 15 days once again, So he will be not able to go back until we did not complete that mission.
Fortunately he could able to level up his avatar and with that he already collected many EXP in that time. Because those monsters continuously attacking him it also became easy for him to collect EXP, but at the same time this also became risky. At any condition he did not wanted his game ever to die because he could lose his loots or even his level. So fighting those monsters he also careful that he did not die.