I connected the trezor T to Adalite and transferred some currency to this wallet but I understand that this wallet is a hot wallet even though it is managed from my trezor so I do not consider that I have my ADAs in trezor T I expected the icon of my Trezor T wallet to appear but it was not like that.
If you used AdaLite then I’m pretty sure they are transferred correctly to your Trezor, but since Trezor don’t support them directly the Trezor wallet probably cannot see them until ADA is supported through a Firmware update in the future. Also see here. It should be possible to use AdaLite to access your ADA on the Trezor, once you connect the Trezor device to AdaLite.