As far as i can see everything is working as you have setup
Here is what you need to do: Set modules to certain pages only specially in this case home page only. You can have other modules in right position in other pages but current module styles belongs to home page only.
Here is how you set modules to pages.
Login to joomla admin panel.
Extensions > Modules Manager.
Now you should see all the modules in your website. Active modules will have a tick mark in status column. Get used to this screen as you will use it a lot.
Now we have to identify the modules as there are no titles in front end. If you know them by names you see in your module list then go ahead and jump to "Assigning Module Positions to pages ".
If you don't know which modules is which few things we can check. Look on right hand side and you will see filters with dropdown boxes. These filters down module list such as list active or list disabled ones or show only certain module positions e.g Header1 module position or show only certain types e.g Image Show GK4 and so on.
So for our example click on "Select Position" and choose "Header1" and you should get one or two modules in the list. Don't forget to set "Select Position" to "Select Position" again to see other modules again or simply click on reset button.
Assigning Module Positions to pages:
I supposed you have find the module, For our example i will be editing module in Header1 position which is slideshow module.
Click on it to edit settings. Now you are in Module settings page.
On left hand side you will see settings for that module.
Scroll down and you will see "Menu Assignment".
Find "Module Assignment" and choose "Only on the pages i selected" for this example.
Click on "Main Menu" Tab and you will probably see ticked check boxes. Now click on "Clear Selection" which is on right to clear all of them.
Click and tick "Home" checkbox only.
Now "Save & Close" module settings.
What we done now is our slideshow will only show in homepage or when home button is clicked.
Do the same with your other modules.
See you around...