lots of help buttons on almost every screen of the program that take you to info. And key word searches of the forum typically turn up lots of good info.
But to reiterate.... Did you SAVE after you made these changes? In Mp3tag's Tag Panel (on the left) you must save your changes for every file. In the column view on the right side it's not necessary. In the columns, when you make a change and move to a different column or file the changes are automatically saved. That isn't the case in the Tag Panel.
There should be a column labeled "Track" on the right side. You can also make changes to the track numbers within that column, and if you're changing several track numbers you'll find it much easier than using the Tag Panel.
I have a feeling that what you're actually looking at is the track number within the filename. If you want the filename to reflect the new track number then you're going to have to rewrite the filename after renumbering the tracks. Easiest way to do that is to use the 'Tag - Filename' converter .