Allow me to explain this chord progression in more detail.
This starts with the chord Ebmaj7, then straight away goes into some non-diatonic chords. These are Abmin9, Dbmin7, Gbmaj7.
This works because even though Ebmaj and Abmin are in different keys they share many of the same notes. Abmin, Dbmin and Gbmaj are also not all in the same key but they all share the majority of the black keys there sound well in the progression.
Playing inversions such as the Dbmin7 with the root at Ab helps give that soulful sound. Having the C directly next to the C# resonates differently than having the chord at the standard position.