'General Discussion' is for looking at broad themes as they could apply to several games. "How do I...?" questions (implementation) go in the Support forum for the engine you are using.
[move]RPGMaker MV[/move]
If you are using pictures, then when you leave a map, your transfer event must include the 'Erase Picture' command, otherwise the picture follows you around.
However, I am a little confused - you start off talking about parallax mapping, then switch to talking about pictures. Those two things are not the same. Could you clarify exactly what it is that you are referring to.
As an aside, I'm not clear why the image you've shown needed to be either a parallax or a picture as it looks like straightforward mapping, but that is a different question.