Actually, I came across the same issue. I needed an image for each category. The plugin add correctly the field image but once the image is uploaded I was unable to print it on the category page.
So I modified the code a little bit. I removed few lines that I didn't need and renamed the function.
You can put the following function in functions.php. (so it keeps the plugin as it is in case of an update).
$arr = categoryCustomFields_DB_GetCategoryValueById($taxonomy,$name);
if($arr->field_type=="image" || $arr->field_type=="file")
$arr->field_value = $arr->field_value;
$b = $arr->field_value;
This returns the root path of my file. I had to remove the beginning of the path (everything before /wp-content) and replace it by the actual site Url.
You can copy this code in the category.php file.
//get the category ID
$cat_id = the_category_ID('');
//Call the new function categoryImage created in functions.php
$url = categoryImage($cat_id,'Image');
//replace the wrong path with the site url
$url= str_replace('/home/fvrepro/public_html', get_site_url(), $url);
//print the image tag
print '<img src="'.$url.'" />';
It's probably a little bit messy and can be improved but it works!
Hope that will help you.