You have to set the destination folder in Options > File Naming > Move files to this directory when saving to the base folder your music files should be saved, e.g. D:\Music
The default is “.”, which means the current folder the files are in, which will lead to your result especially when saving multiple times.
As you have already tagged your files this should be easy to correct. Set the options as described above, and load all already tagged files back into Picard. Picard will use the MusicBrainz IDs it wrote to the tags to load the correct albums again so you can just hit save.