Several questions to find out where you got wrong:
what is the size of the map in tiles?
what is the size of the parallax background in pixel?
what is the filename of the parallac background picture?
what is the size of the picture you're trying to bind in pixel?
Which version of the plugin do you have installed?
what version is your project core?
what version is your editor?
OK, let's start with the first things you did wrong.
1) you never disabled the parallax movement, that is why your actor stands and goes wrong.
Please check the help file on parallax mapping - the background file used for the ground has to have a filename that begins with a ! to disable the parallax (which is a move function, the original meaning of parallax has absolutely nothing to do with mapping).
Additionally, NEVER use spaces in filenames when making a HTML5-based game like MV games. That will cause problems sooner or later because the browser was never designed to handle spaces in filenames.
Rename it to !Map_53 or something like that.
2) not errors, but two comments:
a) your parallax is rather large. It will work on most modern computers, but it will never work on mobiles and older computers with limited RAM might also lag a lot.
b) if you really want to make good maps with parallaxes, you should learn how to use tileset passabilities with parallaxes. To use that region restrict plugin instead for region passability blocks is not only a lazy workaround, you loose a lot of options from tileset passability and have to have an additional plugin that is basically not needed for true parallax mapping.
3) you never answered my questions about editor version and project core version (PROJECT core, NOT yanfly core).
And that could very well be the other cause for your problems because if I remember correctly the bind to map plugin does not work well with later core versions.
4) Kaus has been banned for multiple copyright thefts.
Most people changed to Orange overlay due to that. Orange Overlay was specifically written to use the same functions and configurations as Kaus' Overlay exactly to make replacing the questionable resource with a guaranteed legal plugin easier.
Also why do you have both? Bind picture to map is not needed if you use an overlay plugin
both versions? I asked for two numbers (editor and project core) which might or might not be identical.
also I added two edits to my post above, please read them - especially the one about bindpictureto map being absolutely useless if you have an overlay plugin (and most likely the overlay disables the bind picture plugin as wll)
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