2 part reply.
1. When you create and save a contact, what is your default Save location... Device/SIM card/Google
2. In Contacts > Menu (3 bars) > Settings Contacts > Contacts to display... are you displaying, "All", contacts from your phone? If so, you may want to Save all your Contacts to your Google, (gmail), account in future and select your Google mail address to display contacts or you can use the, "Customised list", instead.
You will need to move some of your contacts to gmail possibly, (Contacts > Menu > Move device contacts to), and then play around with the settings mentioned in item #2 until you get one of everything. Also, you can merge/link duplicate Contacts in... Contacts > Menu > Manage similar contacts.