Signal Change When Oscilloscope is Added
Think about how the input multiplexer works...

If it is implemented with solid state analog switches, then these are really FETs. FET gates are capacitors. Switching the FET involves charging this capacitor. This injects a  spike into the mux inputs and outputs. Depending on circuit impedances, it will result in more or less voltage.

Most analog switch datasheets include a "charge injection" specification for this very reason.

Now, even if it is implemented with relays, consider the fact that the switch connects your probe point to a circuit inside the DAQ board, and this circuit has capacitance. When switching, current has to be drawn from the probe point to charge stray capacitances to the voltage being probed.

You can't measure something without changing it. However, I would presume the NI engineers did their job properly, and inserted enough delay between the mux switching and the ADC acquisition to let these transient phenomena settle before digitizing the input voltage.