Welcome to Android Central! First, make sure the People app on your phone is set to show all contacts. It's possible the contacts that the phone is showing are only the ones associated with the Phone Account, not your Google Account.
Next, go to Settings>Accounts-Google>[your Google account], and make sure Contacts is checked--I'm not sure if that's what you meant by going to the "tools" and checking sync for contacts.
Since people can have multiple Gmail accounts, make sure that the phone is logged into the correct Google account for you.