When adding new smart parts to a portal page it can be setup to be shown on one of the child tabs or listed as a selection item in the more tabs list box.
To ensure that the smart part is shown on a tab make sure that in the portal page smart part selection box it is listed within the 6 smart parts targeting the ‘Tab Control’ target Workspace (assuming default visible tab count).
Any Smart parts listed after the first x will automatically be added to the list box for selection on the client portal.
Ryan Farley pointed out that the value of visible tabs is configurable. More details on this are included in his comments to this Blog post.