To the outside world, you all have the same IP (the IP address of your modem, or your router that functions as a modem). That's not what causes your problems.
I run a home wired/wireless network with a large number of devices (like 15), and I find that network IP address (192.168.x.x) conflicts happen most often with machines that go to sleep or (especially) hibernate, like laptops. I don't have a an I-Phone so I don't know if they do that or not.
What happens with laptops is that they go to sleep with a network IP in memory, but by their sleeping the router forgets they're there, so it can reassign the same number to a device that boots up fresh. Then when the laptop wakes up, looking of the same address, it causes a conflict. The solution is relatively straight forward, at least on my network. You turn off and then restart the device that is showing up with the conflict, and it picks up a new address. Just rebooting won't necessarily release the previously held IP; turning the device completely off usually does.
It can also happen when a printer directly on the network gets turned off, and back on (depending on the printer and how it is connected to the network), as network printers tend to remember their assigned IP (because that's how print jobs are addressed to them) and try to grab it back. If another device has booted up in the meantime and taken that address, that causes a conflict. In that case, you should turn off and restart the other device claimng the IP, rather than the printer.