I take it that by the common name of snook cichlid you are referring to
Petenia splendida.
https://www.google.ca/search?q=pete...dAhUO7Z8KHcbDA0EQiR56BAgKEBY&biw=1600&bih=763
It gets big, 14" or more, so you need big tanks to house it (like a 6 ft. 125 gal. as a bare minimum for an adult).
It has a specially designed mouth to swallow fish. For it's size, it can swallow large fish so anything you house with it has to have large girth.....or it will eventually end up getting swallowed whole.
Tetras not a hard swallow at all......probably no more then a few months of growth for a young snook, and the tetras will disappear.
For a large Central American cichlid, they are very mild mannered and will often get bullied if housed with other large CA cichlids. I'd probably consider housing them with something more mellow like oscars or large sturdy non-cichlids.