When a tree is synced from FTB to the online Family Site, it can be viewed online, and edited by the site creator. To change the so that your site members can edit your synced tree, please see here.
Your tree will be shown on your site to site members and guests according to the privacy settings on your site.
As always, you have full control of who can view or add information to your site.
To edit those settings, please see the following post: How do I make sure all my family site information is kept private?