Can I use my smartphone as a controller for XBox One?
Solution 1:
Yes, you can connect your smartphone to work as a controller, but not without a few caveats. To do so, you need the Xbox One Smartglass app, or if you have a Windows 10 phone, the Xbox app works as well.
As you have noticed yourself, your phone needs to be connected to the same network as your Xbox. It doesn't have to be the same Wifi, though. As long as your smartphone is connected to a Wifi antenna connected to the same home network the Xbox is connected to, it will work. It is possible that you have multiple networks if not properly configured, though. For instance, if your Wifi access point is configured to act as a DHCP server, everything connected to your Wifi will indeed belong to a different network from everything that isn't, while your access point will belong to both networks.
Finally, even if you do manage to connect your smartphone to your Xbox One, you won't be able to play many games. The Smartglass and Xbox apps only offer face buttons, which is A, B, X, Y, Menu, View, the D-pad, and the Guide button (the button with the Xbox logo).
A lot of games would require you to make use of the analog sticks, or the shoulder buttons (RB/LB and RT/LT) as well.
In other words, without an actual controller, your control over your Xbox One will be rudimentary at best. Good enough to watch Netflix, but not good enough to play Halo.
Solution 2:
As already stated in Nolonar's answer a smartphone is not going to be viable for playing games.
However, there are other options if you have the equipment lying around...
It is possible to use an old Xbox 360 controller by streaming your Xbox One through a Windows PC/laptop. I'm not sure about older Windows versions, but the (official) Xbox app on Windows 10 lets you do just this.
The controller either needs to be wired (and plugged directly into the usb port on your PC/laptop) or you will need a wireless adapter. You'll still need your PC/laptop on the same network as your Xbox One.
As well as solving a problem of not having your Xbox One controller, it is also a viable method for playing coop games when you don't have enough Xbox One controllers at hand.