The resolution of this side quest has you initiating a delve during End of Day Phase. When a game effect initiates an Encounter Phase within a different phase, you get the Encounter Phase only. Afterwards, you do not get a Reward Phase and another End of Day Phase.
Because this side quest has the ability to grant 2-3 XP, it's highly recommended that you plan ahead for this and spend all or most of your XP so that you're able to save the XP granted from this side quest, as you won't be able to spend it right away.
To complete this side quest, you are asked to occupy hexes with no landmarks. While the rules don't specifically define towns as landmarks, they are meant to be so. You are meant to land on hexes that are empty in order to fulfill this side quest.