Phantom Voltage on Hot Wire from Another Circuit
The induced voltage you were reading is from the electronic lines of force crossing the non energised conductor creating a voltage (this is how transformers work or inductive coupling) any meter that has a high impedance will detect the phantom voltage, most meters are high impedance or have over 1 mega ohm /volt internal resistance this prevents the meter from loading the circuit and affecting the reading. There are also low Z or low impedance meters that have an internal resistance that is low enough to eliminate the phantom voltage without affecting the measurement. These low Z meters are not sufficient for electronics trouble shooting in my opinion due to the circuit loading. Low z meters are fine for power measurements. you have no problems to worry about. Note if you turn on the light switch after replacing you may see the voltage drop to nothing depending on the type of lamp or load on that circuit.