That plugin is 3 years old. I’m not sure if it uses the menu_order column to set the order but if it does you can filter pre_get_posts or your custom query with:
'orderby' => 'menu_order',
'order' => 'ASC'
This would all have to be done before the $post object is added to the $events array so it would help answer if you added the code that comes before: if ( $events )
Also if you do a var_dump( $event ) somewhere in your foreach loop we can figure out how the posts are being ordered.
Edit
After your comments and looking at the var_dump here is whats going on:
Your getting 5 posts in proper menu order then your break statement causes the foreach loop to start back at 0 then it posts the same 5 posts again. It does this 3 times giving you
1-2-3-4-5 break 1-2-3-4-5 break 1-2-3-4-5 break
See the formated $post array dump: http://pastebin.com/hHPxbzda
If you only want to show the first 3 just add this to your get_posts array:
'posts_per_page' => 3