I've been searching the internet for an answer to this question for a few hours, and what I have found is that most people don't understand the question or the context, and the few that do understand it, don't have a straight answer.
In my case, I started looking into these settings as a workaround to my mobile provider's hotspot restrictions. If your data plan comes with hotspot support, you can simply enable the built-in hotspot or tethering feature of your phone, and you are good to go, but if it doesn't, the most straightforward solution I came up with was this:
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Install and setup a proxy app on your phone. I'm currently using TetherFi, but there are other options. I found TetherFi to be very simple, they will guide you through the process. You still need to enable USB tethering on your phone (but not the hotspot). The key difference is that the hotspot feature of your phone, will ask your data provider if they are okay with you trying to use that service, but your apps won't. The proxy is just another app, that forwards the traffic to the internet. Yes, it is much nicer to have your phone simply redirect all the traffic for you without any proxies in between, but again, this is a workaround without a hotspot-enabled data plan.
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Setup the proxy IP and port details on your client machine, not the router! You basically don't need to do anything on the router as long as tethering is working. I see people trying to setup the router to forward the traffic to the proxy, or installing additional proxies on the router, you don't have to do this.
For example if you are connecting from a Windows machine to the router, enter the IP and port of your phone's app directly in the Proxy settings for Windows. You traffic will go to the router, and because you setup a Proxy, it will "passthrough" the router and go to the phone, where it will be served to the proxy application, which will simply forward it to the internet.
And that's all...
I was basically over engineering this issue, but the solution was much more simple than I thought. Hope this helps someone else out there too.