Using the dCS Mosaic software I can see a little musical note symbol bottom left of the screen - I believe this allows me to ‘phase invert’ the music is that correct?
Is that the same phase convert as to what happens when you swap the speaker cable wire around on the speaker binding posts?
I ask because I am using a Croft Integrated amp which phase inverts and therefore the dCS when selected could possibly balance this out.
The answer is , yes.
However its significance is not straightforward. A major issue is that recordings do not necessarily contain consistent phase ( or polarity) information. Secondly neither do certain speakers where the crossover may , for example, invert the polarity of a drive unit.
Perhaps the most important factor for us as individuals is that sensitivity to such issues varies.I can report that I cannot hear a difference one way or the other. However some say that they find it highly significant.
OK thank you.
As you say its significance is not straightforward - the main thing is that the phase toggle allows me to compensate for the Croft without switching the wires around.
It does but do you really need to do it?
No but it’s comforting to know it’s there. Would “you” happily wire your speakers terminals negative into positive and positive into negative? Perhaps not.
Certainly not unless both of a pair are involved 
.
Either way - it’s much easier to toggle on/off instead of physically swapping the speaker cable on the binding posts. Seeing as the toggle does exactly the same thing.
I would recommend to swap the speaker cable wires on the amplifier side and not the phase on the NWB, since the amp as a whole inverts the phase and no other equipment earlier in the chain will then be affected.
There is a good reason to use the phase swap option on Mosaic in preference.
If you are sensitive to alternative polarities an issue is that there is no consistency from recording to recording and therefore no consistency from end to end. So you should check the connection which is preferable to you for each recording. Using wire reversal this would be tedious. With Mosaic you can just hit the switch and see which you prefer for that album.
Of course for many (most ?) people it will not have any significance. It is also a simple way of finding out if the issue is important to you. I, for example, cannot hear any difference one way or the other.
IMHO in all cases this must have been the decision of the the mix-engineer, mastering-engineer or producer. Who am I to interfere with their professional work?
Having an amp like the Croft turn around the phase is IMHO contrary to good and reliable engineering. RIP Glenn Croft.