wrist detection/notifications

I just bought a new Apple Watch Series 3. I have not received any calls or text notifications since I started wearing it. I have troubleshooted all things available. I finally turned off wrist detection and instantly started working. I understand that this is the only way to make notifications go to both phone and watch. But isn't is possible to just receive notifications on my watch if my phone is locked?

I guess my question is...how should this be working. Shouldn't I be able to get text notifications, calls, etc... on my watch with wrist detection on if I am not near my phone? Is my wrist detection/watch not functioning correctly?

Thank you!