Why do I not see the same dBSPL in Live and in the measurement magnitude?

You might find this article from Charlie Hughes useful for measuring absolute levels using EASERA.

The current functionality of EASERA is to show the measured transfer function, or impulse response, of a system under test (SUT) as if the SUT had been excited by a signal having a level of 1 V.  In order for EASERA to show the transfer function with correct absolute levels, as one might expect when measuring loudspeaker sensitivity for example, please see the article at the link above.

Note that the signal levels shown on the Live tab of EASERA will always be the correct levels if EASERA has been properly calibrated for the measurement hardware that is being used.