I've been involved in IT and Cell Phone sales for 15 years, and I can confirm that not only would you have this strange behavior, but specifically why.
The phone, regardless of whether it's GSM, LTE, EVDO, CDMA, etc. always has a few basic settings to tell it how to communicate with the network. One of these settings is the internet gateway setting. Whether you've got a SIM card or a US-style phone where the settings are on NVRAM in the device, this setting is always present somewhere. The gateway IP is specific to your carrier, and ALL traffic from the phone that isn't considered "local" (inside the netmask specified by another setting in the same place - this would almost never apply excepting possibly some server managed by your mobile provider or a very strange coincidence) go through that gateway to get out to the internet. It's not a VPN or tunnel or anything fancy like that - it's the standard IP protocol itself that causes this. That does mean that you could sidestep it by sidestepping IP, but to my knowledge no one uses ARP packets to communicate directly via MAC address, so that's highly theoretical and pretty pointless.
The reason I'm answering this question when Henning Makholm already covered it pretty well is because it has a potentially dangerous unintended consequence - the traffic is not separately encrypted. That's probably fine if you're in a liberal country and the account is in an equally liberal country, as ISPs usually aren't in the business of arresting people or stealing credit card numbers. If you're coming from or visiting China (or another country known to engage in legal action for what they deem illicit internet activity), you're at risk - even if you're from outside the country in question. The traffic will pass through the public internet in whatever encryption state the destination server requires, through who knows how many different switches and ISPs, until it reaches your gateway, and will then proceed on to its destination from there.
In other words, your traffic is routed first to your mobile provider, then on to the internet at large. It's sent along in whatever encrypted state the destination requests. If it travels through a country that takes offense to your data, and any of that data (even the DNS name or IP in some cases - beware!) can be interpreted (is plaintext or weakly encrypted), you are potentially in serious trouble. So you could theoretically use a foreign SIM to get around the Great Firewall. You could also bake rat poison brownies. Neither are a good idea. Be careful when traveling abroad, and keep those internet searches nice and clean just to be safe.