The rules for Phase III: Arkham Encounters states:
Note that the card may indicate that “a monster appears,” in which case the investigator must either evade the monster (see “Evading Monsters,” page 14) or fight it (see “Combat,” pages 14-16).
Since you have the option to evade it, you don't do have to do the horror check immediately.
Under the Other rules area, you have this about the evade option
Sometimes monsters appear as the result of a location or gate encounter. An investigator can evade these monsters just like any others. However, these monsters never remain on the board after the encounter is resolved. If an investigator evades such a monster, immediately return the marker to the monster cup.