How do I change user account used by the Update tab of AppStore?
You bought the apps with your old Apple ID. Apps are permanently tied to the ID with which they were bought.

I'm fairly certain if you deleted them, and re-downloaded them with your new ID, the problem would be solved. You would, however, have to pay for them again if they were not free.

Relevant questions:

Attempting to update app asks for a different iTunes account password (pretty much a duplicate)

How can I find which account I used for downloading my iOS apps?