I took a backup of my data on my iPhone 6s and then restored it on an iPhone 7. Now there is another SIM in the 6s, but all messages coming in on the 6s are also coming on the 7.
You probably used the same Apple-ID for the new phone, and then all the iMessages get forewarded.
If you want to have a closer look, here is a good explanation of how it works: selfsolve.apple.com
in short, you can do the following steps, to separate the messages on the two devices:
- Transfer your SIM card to your old iPhone.
- Go to Settings
- Tap Messages
- Turn iMessage off
- Go back to Settings
- Tap FaceTime
- Turn FaceTime off