If I understand, you expected that plugging in the headphones would disconnect the outputs to the speakers, much as a laptop or mobile 'phone would, but most or all of these types of boxes would not do that. You will probably have to turn off or disconnect the monitors to stop them.
Some of the larger interfaces contain a mixer that would allow independent software control of levels to headphone and output. I'm almost certain neither the Solo nor the 2i2 have a built-in mixer, I know the 8i6 has.