Normally when this sort of thing occurs, it tends to be a bad digitizer replacement. I had one come into the shop the other day. All went great with the repair, it also tested fully working, dropped it with the customer to get a phone call a few hours later saying the top 1cm of the iPad’s touch screen was not responding anymore…
They also suggest maybe it was a loose connection, but experience has taught me to just get a second replacement part. I’m not sure about the company you used and the policy’s but we offer 3 Months on all our repairs and change the part if it becomes defective over the first 3 months after the repair.
I would speak to the original third party repairer and let them know of the issues and offer them the chance to correct them. The only issue I can see in doing things this way is if they decide the issues are caused by user handling and not due to their part is defective.
Hope this helps you somewhat… :)