Only the contacts entered into your phone as Google contacts (the first pulldown at the top of the page) are saved to your Google (not gmail - that's email only, even though they're the same address) account. If you have them as Phone, Device or SIM contacts, change them. If you can't (it depends on the phone and the version of Android), turn on airplane mode, export the contacts, delete all your contacts (to prevent all of them from becoming duplicated), them import that file - but choose your Google account to import them into.
Now turn off airplane mode and the contacts should sync to Google.
In the future, whenever you enter a new contact, pull that first thing down (tap it) and choose your Google account.