Jpeg file are flat and jpeg file format does not support transparency. Photoshop does not have support for.ai files they can be imported as a single pixels layer that may certain transparency. .Ai file can also be placed into Photoshop document as vector smart object layers. For a Photoshop template you need a layered file like PSD or PSDT. See if there are layered versions of the image you have paid to licence.
If you install Illustrator .ai files are vector files the most likely contain layers. Photoshop does not support .ai file format. Photoshop is a Pixels editor. AI is a vector editor. So your .ai files mat be Illistrator templates.
I do not install Illustrator. Photoshop template are populated with raster images files. I do not use Illustrator I do know how one would use a vector template.