It sounds like you’re wanting the page you are redirected to to display the CPT’s information in a certain way or format, in which case you’ll want to create a single page template for the custom post types you’ve created.
You can use the single.php file as an example for the layout and customize it as necessary, but the name of the file should be single-publicity.php and single-management.php.
I hope that helps!
Edit
I forgot to mention, I don’t know what the name of the page is that you’re looping the CPTs through, but make sure the permalinks don’t conflict (e.g. a page called Publicity with a slug of publicity).