User’s Budget at Completion is not matching the Budgeted Total Cost amounts in activities.

BAC pulls in all the baselined costs. As for BTC, I want to suggest you are looking at these amounts in the activities. I thought you were viewing these figures in the project view; which I don’t think is possible. And yes, when you are changing a resource’s budgeted hours, that will have an effect on the BTC and yes, you would want to change the resource’s budgeted hours which would update the activity’s BTC before you baseline or re-baseline.