Can a baby get accidentally irradiated from an adult person that just came home from radiation treatment?

Depends. If the adult received any type of external beam irradiation (imrt, protons, cyberknife, etc.), then no. If the adult was given a radiopharmaceutical such as radioactive iodine or a temporary internal radiation implant, yes. See: http://www.Cancer.Org/treatment/treatmentsandsideeffects/treatmenttypes/radiation/radiationtherapyprinciples/radiation-therapy-principles-safety-for-patient-and-family.
NO. You received a radiation dose while you were still on the treating table getting external beam radiation treatment. Once the treatment is over, there is no extra radiation energy in you, and you do not carry any excess radiation with you. So, there is no risk of transmitting radiation to someone from external beam radiation therapy.