Are there drawbacks to using a teleconverter from a different brand than the lens?

The biggest concern would be compatibility of the electronics, but this is mostly an issue when using a non-camera brand tele-converter with a camera brand lens. The off-brand teleconverter may not know about some of the communication that the lens and camera do and future firmware updates for either the lens or the camera body may result in further issues if they update the protocol being used. It might also not work as well on future lenses unless the teleconverter itself is updateable.

As far as the quality of the optics go, a teleconverter is basically a magnifying glass that magnifies the image circle made by the lens. It it completely agnostic to the optics of the lens and the lens is completely agnostic to the teleconverter on a basic physics level as long as the teleconverter is properly designed.

Where it does matter is how the lens attempts to focus and what aperture settings are used. Since the teleconverter discards a large portion of the light that would normally make it to the image circle, it causes a drop in the speed of the lens, so the widest open setting goes down.

The compatibility problems occur when the teleconverter can not adapt the focus and aperture signals going between the lens and the camera to ensure they communicate correctly. The degree of compatibility will depend on the precise lens, camera and teleconverter in question though, so best to research for your bodies and lenses prior to making a purchase.