I have never had a problem with this. I don't even really use my GV phone number unless i'm signing up for something.
All phone calls come through to the phone regardless of what number is called, and it only rings a few times, goes to voicemail. Both my GV number and my actual VZW number work the same way and I can't even tell which one is being called (wish I could find a way to do that). All voicemails are sent right to the google voice app on the phone. If someone sends me a text, it shows up in the GV app (there's a setting on the app to send it to the phone's messaging app as well. I don't have any missed calls recorded, or have any notifications, or anything show up in my email account.
Have you logged into voice.google.com (on the computer) and looked at the google voice settings on there? Here are some of my settings:
Phone Tab: Forward Calls to Mobile # checked, nothing else checked
Voicemails Tab: Greeting recorded, transcribe voicemails checked, nothing else checked
Calls Tab: Call Screening-Off, Incoming caller ID-display callers number, Outgoing caller id-dont change anything, nothing else checked.
You can play around with settings to see how they work for you. Sorry, I didn't have a link to anything instructional for you.