To do this in egit you need to adjust the push settings for the given remote:
Team -> Remote -> Configure Push to Upstream
This will display a dialog called "Configure Push". In the "Ref Mapping" section you can specify what you want to push.
If you want to push all tags, click the "Edit (Advanced)" button. This will display a sub dialog called "Push Ref Specifications". From here you can indicate that you want to push all tags by clicking the "Add All Tags Spec" button.
If you only want to push specific tags, rather than all, you would have to add the refspecs one at a time in the "Configure Push" dialog, by using the "Add..." button at the bottom the "Ref Mapping" section. For the 'Local Branch' just start typing the tag name and egit should offer to fill it in from a menu. It should end up as something like refs/tags/some-tag-here. Then use exactly the same string for the 'Remote Branch'.