@WordUpHey
What I think it is, is there are values in the Database that have not been updated. You may have updated the Site Name and Blog Address in the database, but that does not update values for the rest of the tables.
My suggestion, and you should back up the database before trying this...
Go to the new site and install a plugin: Find and Replace by Frank, Inpsyde GmbH.
I created a video over a year ago that walks a person through using this plugin. The video can be found here: https://vimeo.com/68300949. Fast forward until 11:29. Follow the steps and report back.