The short answer to this question is that with a non-T-Mobile phone, you're on your own. I doubt that the necessary proprietary OS hooks will be available via updates.
It is possible (in some cases) to get wifi calling on a non-T-Mobile phone, but your phone must be using a T-Mobile based ROM (firmware). For example, I have an unlocked/rooted Samsung Galaxy S3 model SGH-I747 (sold by AT&T). After conducting extensive research, I found that I was able to install a modified T-Mobile stock ROM on my phone (a stock ROM is the software package that is distributed by the carrier). Since it is based on a T-Mobile stock ROM, it has the T-Mobile proprietary software that allows me to make calls via wifi.
When I activated my T-Mobile account, the Representative at the T-Mobile store warned me that she could not guarantee that I would get the full functionality on a non-T-Mobile phone, and specifically said that wifi calling would not work. Although I knew otherwise, she did her job correctly by setting the expectations from the outset.
Depending on type of phone you have, wifi calling may be possible. However, you need to be prepared to find a compatible T-Mobile based ROM and flash it to your phone. I would not recommend doing so unless you are a power user, and are comfortable with computers, smartphones, rooting, and flashing ROMs. One mistake could render your phone permanently useless (although you can usually recover it). Proceed at your own discretion and risk.