If I set up a VPN connection on my iPhone running iOS 10.3 and then connect a device to the iPhone’s Wi-Fi hotspot, will that device’s traffic also be sent over the VPN?
Visit https://icanhazip.com from your tethered device and report back 
Have you selected “Send all Traffic” within the VPN (iphone) settings? If so, then yes your traffic is going across the VPN tunnel. If you disable Send All Traffic, your iphone will only use your VPN connection if the private ip range cannot be found with other connections (such as; wifi, cellular etc…) so, another trick you can utilize on an iPhone is to configure it with a configuration profile using the apple device configurator from the mac app store.
Be careful. If a live connection gets slow iOs will snap over to another live connection without telling you. It is very aggressive in doing this (to solve the faceTime parking lot problem). Also, there is nothing stopping an App from ignoring your wishes (if it wants to) and sending data over what ever live interface it wants to. If you want to turn off cellular and run over wifi only then you are better off.
Haven’t set up my VPN yet. Was hoping someone already had an answer. I probably will test and report back in the next couple of days.
Where is this setting?
nothing stopping an App from ignoring your wishes
You have a source for this? Because networking is something that’s handled at a rather low layer of an Operating System and it really shouldn’t be possible to “ignore” whatever IP routes are known to the kernel.
I actually tested this just 2 days ago. Short answer NO.
I was connected to my OpenVPN server on 4G (my home router) which redirects that particular login credential to a Romanian VPN datacenter. Verified easily via wtfismyip.com that 4G was on Romania. Then when I turned on hotspot and connected my laptop it showed the hotspot connection was using my regular Verizon ipv4 and ipv6 addresses and not going through VPN.
Not sure on the specifics and why it opens the hotspot stream not through OpenVPN just yet.
Work around. Just use OpenVPN on the device your using to connect to hotspot on phone and it should then send data through VPN. I didn’t test that part as it was a family members laptop that I didn’t feel like installing OpenVPN on and importing a profile.
It is an ios setting that (I think) is on by default called WiFi assist. If your wifi gets slow it will switch to cellular really fast (if it can’t find another access point that it already knows). They did this so you can walk out of a building and into a car without interrupting a facetime session.