Even the tip of trying to "hit up on the ball" isn't universal. I might say that to a player who was bending at the waist too much and effectively pulling down through their serves. One of my kids hits her serves with a lot of spin though, since she already knows how to hit "up on the ball" just fine. I'm actually trying to coax her to hit a little more "through the ball" so she can generate some pace when she needs it.
The tip or the image that a teacher uses to promote one action or another is almost completely dependent on what that player is already doing if that guidance is actually going to be constructive. This might be my round-about way of saying that you're probably hitting up on the ball just fine.
Also keep in mind that there are significant differences between serving a tennis ball over a 36"-40" net and serving a volleyball over a net that's... hmm... well, it's sure higher than six feet! The volleyball has to get up over that high net from the top of our reach, but the tennis ball has to get down over that much lower net starting from a point well over a foot higher than the top of our reach (remember that a standard racquet is 27"). While that volleyball physically requires a little upward drive to clear that net, not so much at all in the case of the tennis serve.
What is sort of interesting to me is that the volleyball serve doesn't benefit from the extra mechanical element that we get in a tennis setting when wielding a racquet (the racquet head can fly faster than a v-ball server's hand). I'd say that this makes the volleyball serve a very good illustration of how much power can be derived from the legs and core for that general motion. Guess I've gotta tune in on some volleyball coverage now...