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.
[Update]
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.