Hi Kyle,
I think you may have stumbled upon a potential bug, which I had to investigate in more details. The problem is, that the incorrect uploads folder is returned on the sub-site. The main site folder should be used, however WordPress returns the sub-site URL for some reason.
It tooke me a while to figure it out, and I think there is an issue with WordPress itself, as the method taken from their documentation does not work as intended, so I had to make a bypass solution.
I could only test this modification on one multisite network, but I am hoping it will do the trick permanently. Please follow the steps below carefully:
Please note: Before editing any files, please make sure to have a full site back-up just in case! If you need help with this, you can add temporary FTP access, and I will do it for you.
1. Open up the wp-content\plugins\ajax-search-pro\includes\classes\core\class-asp-manager.php file on your server via FTP
2. Replace the file contents entirely with this: class-asp-manager.php
3. Save the file
4. De-activate the plugin in the plugin manager
5. Activate it again (network activate)
6. This might not be neccessary, but: Open any of the search instances you created and just hit the Save all tabs! button, without changing anything.
7. Clear your site cache/browser cache, and it is done.
Now the layout should be fixed and visible on each multisite blog. Please let me know how it goes, as if this works, I will include it as a permanent fix in the upcoming release.