When you have group mode set on a wiki, each group has their own page(s) within the activity.
When the wiki is set to visible groups the students in one group will only be able to edit their own pages and will be able to use the "Other Wikis" dropdown at the top right of the page to view the other group's pages (but not contribute).
When the wiki is set to separate groups the students won't have the "Other Wikis" dropdown (but Admins and the Teacher do as they have the "access all groups" permission).
Students should be able to see what you contribute (depending on what page you posted to and the group mode).
If this doesn't make sense can you provide a screenshot of the settings page?
I hope this helps