Samsung has already confirmed that it will be possible to use Samsung Pay on Gear S3 even when you pair it with a non-Samsung smartphone. In order for the mobile payment service to work, the device needs to be running Android 4.4+ or later software / firmware.
According to the Samsung Pay official Twitter account you can use the service with non-Samsung devices as of today. In order for this to work a new update for the Gear Manager app is being currently pushed out to different markets. It may take it a little while to reach you, so please be patient.
Here at Tizen Experts, we did have an update earlier today, but the Gear Manager app remained at the same version number, version 2.2.16101261. Has anyone else experienced this ?