Cross-site linked copies: TBP changes are not propagated to the destination

I did a cross-site linked copy of the "Publications" page (std demo package). I published the destination site. Then I modified the TBP on the source for one of the tree present container (start date suddently fixed to tomorrow). The source site correctly only display 2 "publications" in live mode. But on my destination site I still have three object in live mode.

I flushed the cache. No change.