Often rebound relationships can be a band aid solution for the pain and hurt inflicted by the previous lover. If the person getting involved in the new relationship was the one to end the old one, I would be less worried. Usually people have been thinking of ending a relationship for ages before the event actually happens. By the time they get to finish it, they may have worked through their feelings and be ready to move on.
This doesn't apply to the person who didn’t instigate the previous breakup and becomes quickly involved in a new relationship. Some people cannot bear to be on their own so will flit from person to person in an effort to avoid dealing with the issues leading to the breakup. They are used to being part of a couple. They have an inherent need for someone to love them and need them and hence they can become deeply emotionally involved very quickly. Ironically this is often the reason for the rebound relationship breaking up as the new partner feels swapped by the level of neediness.
It is worth noting that often someone on the rebound often isn't even aware of what they are doing. They are hurting emotionally and mentally and can crave comfort from another human being. This can mean that they end up in a relationship for the sake of having somebody to hold rather than to be with that person. Their new partner can get very hurt as the realisation sets in that they aren’t loved for their individuality as much as the fact they can provide a quick fix solution to a painful situation.
It is always wise to date people who have just come out of a relationship with care. Take things slowly and try to make sure that it is you they are interested in before becoming emotionally involved. Everyone needs time on their own particularly if they come out of a long term partnership.
It is a little like grieving - there is a process that you must go through in order to emerge a stronger person at the end of it. For most people divorce and the breakup of a partnership means the end of a dream even if you were the one to instigate the break up. Everyone will have some feelings of regret if only for not having the fairytale ending.
If you do find yourself involved with someone who you suspect is on the rebound, gently advise them to spend some time on their own working through their emotions. Encourage them to date other people. Keep in contact with them if you are interested in a long term relationship. If you two are destined to be together, it will happen although maybe not right away. This is really the only way to ensure how a rebound relationship can work for you.