In order to allow you to show/hide particular tiles from certain groups, LiveTiles takes advantage of SharePoint groups within the Design canvas for you to acheive this.
Step 1: Go to the design canvas and drag a tile onto the page.
Step 2: Go to the tile settings and go to the advanced tab.
Step 3: Choose either Except for or Only for depending on what result you want from the tile.
Step 4: Select the group and click on the plus in order to add them to the list of people you want to see/not see the tile.
Step 5: Save the tile, you will see an option in the top right allowing you to view the page from the view of different groups showing you how the page looks without the tile.
In addition, LiveTiles supports nesting Active Directory groups in SharePoint groups, allowing you to be able to Hide/Show tiles for Active Directory groups.
In order to set this up, you will need to change the following permissions to the following:
Once you have allowed it so only members of the group can view, AD groups in sharepoint groups will be enabled once the following permission is checked. If it is not, then AD group targeting will not work.
In addition, this will not work if the user is in the Admin group, as Admins will be able to see all content regardless of what groups they are in.