If Michael wanted to send a public "message," he would have had Tessio killed in the car and had his body left where it could be found, like a shot across the bows of the other gangs (as was Paulie). But since he intended to whack all the other Dons, I'm guessing that Tessio was taken to some secluded place, shot in the back of the head, and buried somewhere that his body could never be found, so that Michael's "legitimacy" move to Nevada wouldn't be clouded by having the body of a close associate turn up murdered.

Of course, Olivant would say that Manolo the gardener did it and buried him in the rose garden. Nice crop that year.