Thanks, that image is indeed helpful.
The ExifTool command will correctly remove the quotes and split the single long keyword to individual keywords.
However the keywords are stored as an old/depreciated IPTC:Keyword category, rather than in the expected/current DC:Subject category.
Therefore a change in the command is required:
exiftool -r -sep ", " -tagsfromfile @ -keyword 'MacOSPATHtoFILEorFOLDER'
exiftool -r -sep ", " -tagsfromfile @ -keyword "WinOSPATHtoFILEorFOLDER"
These commands will create a new file, the original filename will be changed to include _original at the end of the name. An additional command can be included to -overwrite_original files (work on copies, create backups and test thoroughly before doing so).
You could also copy the legacy Keywords metadata into the Subject metadata, that way both old and new applications are covered:
exiftool -r -sep ", " -tagsfromfile @ -keywords '-subject+<${keywords}' FILEorFOLDER
A bit late but here is a Bridge script for the same 
#target bridge
if( BridgeTalk.appName == "bridge" ) {
sepkeys = MenuElement.create("command", "Seperate Keywords", "at the end of Tools");
}
sepkeys.onSelect = function () {
var thumbs = app.document.selections;
if (ExternalObject.AdobeXMPScript == undefined) ExternalObject.AdobeXMPScript = new ExternalObject("lib:AdobeXMPScript");
var FolderName = decodeURI(Folder(app.document.presentationPath).name);
for(var a =0;a<thumbs.length;a++){
var selectedFile = new Thumbnail(thumbs);
app.synchronousMode = true;
var xmp = new XMPMeta(selectedFile.synchronousMetadata.serialize());
var keys = getArrayItems(XMPConst.NS_DC,"subject");
if(keys.length == 1){
xmp.deleteProperty(XMPConst.NS_DC,'subject');
keys = keys[0].toString().replace(/"/g,'').split(",");
for(var k in keys){
xmp.appendArrayItem(XMPConst.NS_DC, "subject", keys.toString(), 0,XMPConst.PROP_IS_ARRAY);
}
var newPacket = xmp.serialize(XMPConst.SERIALIZE_USE_COMPACT_FORMAT);
selectedFile.metadata = new Metadata(newPacket);
}
}
ExternalObject.AdobeXMPScript.unload();
ExternalObject.AdobeXMPScript = undefined;
function getArrayItems(ns, prop){
var arrItem=[];
var items = xmp.countArrayItems(ns, prop);
for(var i = 1;i <= items;i++){
arrItem.push(xmp.getArrayItem(ns, prop, i));
}
return arrItem;
};
};