What does it mean when a lamp (converted to a "touch" lamp) comes on by its self when garbage disposal's on?

My mom is in a home that was built in 1922. She has suffered from the occasional blown fuse. Now, she is concerned about a lamp that comes on by its self when certain appliances are turned on in another part of the house. This next fact may be important. The lamp is a standard lamp. However, it plugs into a device that converts the lamp to a "touch" control. The lamp is in one room, while the garbage disposal is in the kitchen (of course). I have not noticed any dimming of lights in the house. I think that this lamp also comes on when the vacuum cleaner is plugged in and used upstairs. Any help would be appreciated.