I am not an expert on parrotlets, but they did come up a few times when researching parrot aggression and territorial behavior in general. All parrots have the potential for cage aggression or other signs of territorial behaviors. The root of the behavior is usually instinct-driven, so it can be hard to re-train once it becomes in-grained. However, husbandry skills, environmental factors, and individual temperment can make a big difference on how much of a problem it will be with any particular bird.
Some parrot species are more prone to territorial behaviors, including parrotlets. Other species that are commonly cited as having strong territorial instincts include Amazons, mini-macaws, Quaker parakeets, some conures, and African grey parrots. But really ANY parrot can show this kind of guarding behavior. Sometimes it involves protecting the cage or a favorite perch or its food dishes. Other times, the focus might be its favorite person, favorite toy, its mate (or whatever it perceives to be its mate), or another bird that it is closely bonded to.
Protecting what you consider valuable from intruders or rivals is pretty core behavior, regardless of species. Plus parrotlets tend to form strong bonds and they are fiercely loyal, so it is not surprising that they would be willing to defend what they love from any threat, large or small.
It is important to recognize that there is a link between territorial behavior and hormones. Breeding tends to increase the desire to defend the nest and protect their mate, so cage aggression can become worse when the bird is in breeding season. If your bird is showing other signs of hormonal behavior, decreasing the hormones might help reduce cage aggression too.
However, cage aggression is not always driven by hormones. The root cause can be related more to issues of security and trust. As sunnysmom already mentioned, if your hands are seen as a threat, then you are more likely to encounter cage aggression when you reach into the bird's cage. Your hands are scary and unwelcome. It's a defensive behavior, so if you respect your bird's territory and personal space, they are less likely to feel a need to defend their cage or their body from your hands. Ideally, you want to build up trust and learn to read body language so your bird will feel comfortable allowing your hands into his cage, when necessary. Respectful hands are not as scary as pushy or grabby hands.
If your bird does end up displaying cage aggression, there are various approaches, depending the current situation and the severity of the problem. One possible strategy for curbing territorial behavior involves switching to a two-cage system, so the bird spends the day in a large, toy-filled "play cage" and then gets transfered to a smaller, less busy "sleep cage" at night. This provides the parrot with a routine that encourages peaceful cage-transfers and also takes the pressure off trying to access the cage while the bird is inside. You can clean and service the night cage while your bird is playing in his day cage and vice versa. Not only does this allow you to respect your bird's personal space, but it means that you don't need to stick your hands into a tight cage with a pissed-off and scared bird all the time.
It's a win-win.