You could build a SQL query using $wpdb containing all your post IDs from the array that will list all the terms. Or even better get the post IDs in the same query instead of getting them from the array you mentioned.
This is an example:
global $wpdb;
$query = $wpdb->get_results( $wpdb->prepare( "select * from `$wpdb->term_relationships` where object_id IN (select ID from $wpdb->posts where post_type="%s" AND post_author = %d)", 'some_custom_post_type', get_current_user_id() ), ARRAY_A);
print_r($query); and have a look at the return value. Since get_results is used with ARRAY_A it will return an associative array with the SQL results.
I haven’t used a JOIN in the SQL query example to make the query easier to understand, but using a JOIN will be even more efficient on the DB side.
LATER EDIT:
An example SQL JOIN query that does the same as in the answer above would be:
SELECT wp_posts.ID, wp_term_relationships.term_taxonomy_id, wp_term_relationships.term_order FROM wp_posts INNER JOIN wp_term_relationships ON wp_posts.ID = wp_term_relationships.object_id AND wp_posts.post_type="some_custom_post_type" AND wp_posts.post_author = 1
In order to get the SQL query executed through $wpdb, you need to change the “wp” table prefix so that the tables are addressed with $wpdb->table_name, WordPress will take care of the prefix change after that. Then the query becomes:
SELECT $wpdb->posts.ID, $wpdb->term_relationships.term_taxonomy_id, $wpdb->term_relationships.term_order FROM $wpdb->posts INNER JOIN $wpdb->term_relationships ON $wpdb->posts.ID = $wpdb->term_relationships.object_id AND $wpdb->posts.post_type="some_custom_post_type" AND $wpdb->posts.post_author = 1
Then you include the SQL query in the $wpdb->get_results method using ‘prepare’ method also, and you end up with:
global $wpdb;
$query = $wpdb->get_results( $wpdb->prepare( "SELECT $wpdb->posts.ID, $wpdb->term_relationships.term_taxonomy_id, $wpdb->term_relationships.term_order FROM $wpdb->posts INNER JOIN $wpdb->term_relationships ON $wpdb->posts.ID = $wpdb->term_relationships.object_id AND $wpdb->posts.post_type = %s AND $wpdb->posts.post_author = %d", 'some_custom_post_type', get_current_user_id() ), ARRAY_A);
Experiment with what I suggested in the answer, and then go ahead and try the join way. Please don’t forget to accept the answer if this helped you!
For more information on SQL JOINs, go here http://www.w3schools.com/sql/sql_join.asp
For more information about using wpdb class instance and methods, go here: https://codex.wordpress.org/Class_Reference/wpdb