Hi
Apple Watch Series 3 (GPS + Cellular)
For an Apple Watch Series 3 (GPS + Cellular) that has been purchased from Apple or an Apple Authorised Reseller in the US, subject to having a compatible service plan for your iPhone (which must be an iPhone 6 or newer model, running the latest version of iOS) that includes support for the watch, you will not have an issue with connecting your Apple Watch to T-Mobile.
In respect of its built-in cellular feature, Apple Watch Series 3 (GPS + Cellular) is not locked to any specific carrier. It has a built-in eSIM that copies information from the iPhone's SIM card. It currently be used in the US with a compatible plan from any of AT&T, Sprint Wireless, T-Mobile USA and Verizon Wireless:
Apple Watch - Carriers - Apple
In order to be able to use the built-in cellular feature, you will need a service plan for your iPhone that specifically includes support for the Apple Watch, including your carrier activating the watch on the plan. An activation fee and ongoing monthly cost may apply.
T-Mobile advises that support is available for the watch with T-Mobile ONE plans - for more information, contact your carrier:
https://www.t-mobile.com/offers/apple-watch-series-3-support
Follow the instructions here to set up your Apple Watch and enable the built-in cellular feature:
Apple Watch Series 3 (GPS + Cellular) can also be used without activating the built-in cellular feature, in which case it functions like a GPS-only model.
Apple Watch Series 3 (GPS)
Apple Watch Series 3 (GPS) can be used in conjunction a service plan for your iPhone (which must be an iPhone 5s or newer model, running the latest version of iOS) from any carrier.
More information:
Apple Watch - Compare - Apple
How to use your Apple Watch without your iPhone nearby - Apple Support
About Bluetooth, Wi-Fi, and cellular on your Apple Watch - Apple Support