updating values in one table if depending table row is affected
Not sure if this will fit in your situation, but a mysql VIEW should work for you, and make things easier. 

You could create a VIEW called product_table, based on a select over subscriber_table, like this:

CREATE VIEW product_table AS SELECT item_id, product_id, COUNT(*) AS
count_subscriber  FROM subscriber_table GROUP BY item_id, product_id


Using this, you will not need to update manually product_table data on every change made over subscriber_table.