Why do EOPs affect both ECI and ECEF in the Orbit Propagator simulink block?

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I am using an Orbit Propagator (https://au.mathworks.com/help/aeroblks/orbitpropagator.html) in Simulink.
According to the documentation, "Numerical integration, however, is always performed in the inertial ICRF coordinate system."
I run it with and without using EOPs to check the difference. The output of the block is ICRF/ECI, and I convert it to ECEF using the ECI->ECEF quaternion from the block output as well as including Earth's rotation.
When I compare the two cases, it appears that EOPs change both the ECI and the ECEF values.
Since the EOPs are used to convert between the two frames, shouldn't one set of coordinates remain unaffected, while the set of coordinates in the other frame are affected by EOPs during the coordinate transformation?
For example, if the propagator internally computes in ECI, that ECI output should not be affected by EOPs. The EOPs would affect the output quaternion ECI->ECEF, therefore affecting the values in ECEF. And the other way around: the block internally computes in ECEF, then the block output in ECI would be affected by EOPs, but not the ECEF.
Is my understanding correct?
Why do the EOPs affect both coordinate frames, instead of the derived one only?

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