Communication between Apple watch 4 and iPhone

I recently got the Apple Watch 4 and iPhone XS. I wantrd the option of leaving my phone at home while I went off to work and still being able to use my watch to talk and text on. However, I found this to be difficult because whenever I left the phone at home, when I got to work, I'd find that my watch was unable to make calls or texts. If there is anyone that can verify why I think this is true let me know. I think it's not working because my iPhone is sitting at home connected to my wifi home network off my router and then while I'm at work, my Apple watch is connected to my cell network of my cell service provider. (Verizon). Does my iPhone need to be on my cell network while I'm away long distances with only my Apple Watch(which is also connected to my cell network?)

So what I'm saying is that if my phone is miles away at home connected to my home wifi and I have my Apple Watch which is connected to my cell service, then they can't talk to each other because they aren't on the same network?

So everytime I want to leave my iPhone at home, and only take my Apple Watch with me, I need to make sure I shut off my iPhones wifi.....so it'll connect to my cell service by default and be allowed to communicate with my watch being that they'll be on the same cell network.

Is this true??? Because i can't find this anywhere on the web. This Verizon help page almost cons the issue but not quite.

Any help or verification would be great. I've tried it a few times and out seems to be true....unless it's just coincidence that my watch never works on its own when I don't disengage the wifi on my iPhone. Anyone else have this issue?