containers are not part of the module but of the tabmodule (module reference) data, which is derived from the page instead of the copied module by design.

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Cheers from Germany,
Sebastian Leupold

   

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You can also check out the Advanced Control Panel by Oliver Hine.
http://oliverhine.com/DotNetNuke/Administration/AdvancedControlPanel.aspx

 I don't believe it does it any differently, but there is an option to select the container that you would like to use when you add it to the page. It also lets you choose if you want to add a copy of the module (changing content in one won't change the content in the others that you copied it from) or add a linked module (changing content in one changes all linked modules).

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