@ Jessica
Well, best guess… the version of MySQL installed in the host is outdated. What version is installed? I ask because your local install must be a more recent version because it supports InnoDB and FULLTEXT. When Connections installs it creates its custom table based on the supported features of the MySQL it is being installed on for maximum efficiency. So, this is really a server config issue, not really a Connections bug or limitation. When pushing from a local (or server to server) the software stack should be setup to be similar as possible.
You have two options…
One, update MySQL on your production server. If it is update to date enable the InnoDB engine (which is by default on install, so it would have been disabled intentionally).
Two, on your local install… go to the Connections : Settings admin page and click the search tab and disable the FULLTEXT option. Then go to phpMyADmin on you local install and change the table engine from InnoDB to MyISAM (the default table engine in older versions of MySQL).
Hope this helps! Let me know.