Could my template be rendered with shuffled modules positions?
Based on the template your are using and specific CSS styles when you open the Modules Dashboard the rendering of modules and position could be overlapping.
This is related to the specific template and layout used on your site and can't be controlled by an external application such as Visual Styles Modules. If you experience difficulties to locate modules position for your template a possible solution would be correct elements styles using the Styles Dashboard to improve displacement of modules.