Assign author on ajax wp post insert

You’re almost there. Here’s the part that is setting the author of post to user with ID = 1:

    'post_author' => 1,
    'post_status' => 'publish',
    'post_type' => 'testimonial',
    'author' => $current_user->ID,

You even try to set the author to $current_user, but you don’t initiate this variable anywhere in your code and you set author field instead of post_author.

So here’s the correct version:

    'post_author' => get_current_user_id(),
    'post_status' => 'publish',
    'post_type' => 'testimonial',