I used to teach the transition between a roundoff and a backhandspring as being closer to a punch than a jump, but I've backed off of that lately, and now teach a deliberate bend in the knees on landing between the two skills. Here's why:
In order to get a long, low, fast backhandspring, the gymnast's center of mass needs to be significantly behind the feet when she initiates the BHS. By bending the knees, she allows a slight delay between landing the roundoff and initiating the BHS, and during that delay the CoM can fall further behind the feet, allowing for greater horizontal acceleration. I've also found this method extremely effective to avoid the forward knee buckle you often see in low-level backhandsprings; rather than emphasizing a fast RO-BHS, I emphasize a long one, and often tell kids I want them to make this transition slower (which, counter-intuitively, results in a faster BHS).
Whether you want to call it a jump or a bounce or what is as much a semantic question as anything else. The gymnast bends the hips and knees, then pushes off the floor with the glutes and quads. To me it's more like a jump than a rebound.
EDIT: To clarify, the amount of bend and the speed of the transition will vary depending on the tumbling surface. Gerald George has an excellent breakdown of this is Championship Gymnastics (I feel like I'm recommending that book in almost every coaching discussion these days). THe slower the response from the tumbling surface, the less the knees should bend in the transition. For example, a gymnast tumbling on a competition floor will need to bend her knees more than a power tumbler doing the same sequence on a rod floor. On a tumbletrak, there should be almost no bend at all.