Mental Manipulation (also known as Mind Control, Brainwashing, and Compulsion) is the concept that the human mind can be altered or controlled by certain psychological techniques.
Brainwashing is said to reduce its subjects' ability to think critically or independently, to allow the introduction of new, unwanted thoughts and ideas into their minds, as well as to change their attitudes, values and beliefs. The user must be in close proximity wit the victim, and then it is possible to control their minds and thoughts. Once the victim is in this hypnotic trance state, they can then be manipulated to do anything the master desires. In some cases, they can be manipulated to hurt others or themselves, including committing suicide.
By prefacing a statement with "I heard a rumor," Allison can compel people do whatever she desires. Although she initially abused her power by using it for personal gain, her ex-husband, Patrick caught her using the ability on her daughter, Claire and she realized her use had been exploitative and stopped using it unless she had to. However, in order for her power to have effect she must be close enough to a subject that they can hear her.
Lila is able to mimic the powers of the Umbrella Academy, at least while in close proximity to them and typically use these powers with great skill. During her fight against Allison, Lila was able to use her reality manipulation powers against her to make her stop breathing. Interestingly Lila was able to manipulate her without first saying "I Hear a Rumor" first. As seen where when Allison attempted to manipulate her and first to say "I Heard Rumor", Lila was able to compel her to stop breathing by following up her command before she could say her own.