WordPress Allows contributors to see and manage only their custom post types and drafts from the manage posts screen.

functions.php

/*
 *
 * Allows contributors to see and manage only their custom post types and drafts from the manage posts screen.
 * src: https://wordpress.stackexchange.com/questions/89233/restrict-contributors-to-view-only-their-own-custom-post-types
 *
*/
add_action( 'pre_get_posts', 'aet_filter_cpt_listing_by_author' );
function aet_filter_cpt_listing_by_author( $wp_query_obj ){
    // Front end, do nothing
    if( !is_admin() )
        return;

    global $current_user, $pagenow;
    wp_get_current_user();

    // http://php.net/manual/en/function.is-a.php
    if( !is_a( $current_user, 'WP_User') )
        return;

    // Not the correct screen, bail out
    if( 'edit.php' != $pagenow )
        return;

    // Not the correct post type, bail out
    if( 'tribe_events' != $wp_query_obj->query['post_type'] )
        return;

    // If the user is not administrator, filter the post listing
    if( !current_user_can( 'delete_plugins' ) )
        $wp_query_obj->set('author', $current_user->ID );
}