When you import and view Microsoft Word files, they are being rendered by the built-in web viewer of iOS. The problem is likely caused by the way the Word file was authored. You may have used a font that is not directly supported in iOS.
When iOS displays the file, it will substitute fonts for the ones that are available. Because chord charts authored in Word typically use spaces to align chords over lyrics, the alignment of these chords may shift due to the metric of the replacement font. Because space characters are so much narrower than other characters in variable-width fonts, the author uses many more spaces to align text. The width of characters when different fonts are used is the reason the chords will not align.
Additionally, because the Word file is being viewed by a product not written by Microsoft, you will likely get different results.
OnSong works best with text-based chord charts and lyrics. We recommend converting your Word file into text and then adjusting its chords in OnSong. This will grant you the usage of the best possible features and functionality of OnSong, like being able to transpose and highlight chords.
Otherwise, we recommend outputting the Word file as a PDF and importing that file instead. PDF files maintain an exact representation of how a file is printed and may give you better results.