Yes. Content (including extracts) are never shared across sites. So the default "easy" option is to refresh the extract twice. And if this is burdensome, then there are other options such as writing a script that does replication across sites. One such example would be to use tabcmd. Do a tabcmd login on site1, then do a tabcmd get (which downloads the extract from site1). Then do a tabcmd login to site2, then do a tabcmd publish of the extract that you already downloaded.
Thanks for clarifying that Jeff!