Technical question on phase inversion.

This past weekend, I replaced my solid state preamplifier with a tube preamp. What a difference! I really like the change in the sound but I'm confused by one thing. The MFA Magus B manual says this about the main outputs,  "NOTICE: The high-level stage of the Magus preamplifier is an inverting amplifier. Many audiophiles prefer to correct for this by reversing the speaker cables on BOTH speakers (+ to - and - to +)." So, now I'm confused! I have tried it both ways and they both sound good to me. I'm wondering if there is a rule of thumb about "inversion" that I'm not aware of. So far, I'm only listening to CD, if that helps. Don't get me started on how to correct for inversion when playing analog. That's my next adventure!
 Your pre amp inverts phase. Many tubed pre's do. Many recordings are not actually " in phase" , tho' I think that the majority are. I would just swap your speaker connections as per your manufacturers instructions be content knowing that  youll be " phase correct " the majority of the time.
If using a sub on the same wall as your mains invert it's phase too
Roughly speaking, 50% of all recordings are 'phase inverted'. If the recording is multi-miked and multi-tracked, its going to be really hard if not impossible to hear the difference.
The audible significance of inversion or non-inversion of polarity, aka "absolute phase," is controversial. In part because many recordings are comprised of a random mix of polarities for different instruments and/or singers. Consistent with Atmasphere’s comment, it is most likely to be significant on the relatively few recordings that were engineered using "purist" techniques, meaning just two or three microphones and minimal post-processing.

Interchanging + and - on both speakers (or on the corresponding output terminals of the amplifier) will of course compensate for the polarity inversion your preamp imposes on both your CD and vinyl sources. However if the CD player is also known to invert polarity (which would probably be mentioned in the measurements section of Stereophile’s review of the player, if they have reviewed it), and your phono stage does not, then you would not want to interchange + and - on the speakers. Instead you could make everything come out correctly by interchanging the cartridge connections for each channel (i.e., interchanging white with blue, and interchanging red with green).

-- Al

Thanks for your responses, so far. I gather that "absolute phase" is not really absolute, as it can change with the recording and even the source component can play a part. I doubt that my Oppo 105D contributes to the polarity inversion, but who knows (LOL). In any case, it just feels strange to reverse the cables on the speakers. Based on your comments, and the manufacturer's suggestion, I'll leave them reversed. Thanks for your explanations and suggestions. 
We always get into the same phase lock loop. Lol. The guy who has studied this whole absolute polarity the most, George Louis, the Polarity Pundit, says that of the audiophile recordings one normally thinks of, you know, the RCA Living Stereos, the Mercury Living Presences, Deutches Grammophons, Opus, Proprius, you know, things in that vein, almost all of them are inverted in polarity in the CD versions but not so much at all in the analog versions. So, for digital it’s not 50%. Not even close. Has anyone actually listened to an RCA Living Stereo CD? Yuk!
If the issue is really bothering you, buy a copy of the  'CHESKY RECORDS
JAZZ Sampler
Audiophile Test Compact Disc
VOLUME 1'.  It includes a few Absolute Polarity tests, to enable you to see if you can detect the difference(s) with phase inverted, along with other tools to help you properly set up and test your system.  If you can't audibly discern phase inversion with this CD: don't worry about it.    If you can: it will enable you to make the corrections necessary for your greatest listening pleasure.  Of course, then you'll have to listen to every recording in your collection and mark some for phase-reversed listening(if there's a reversal switch, somewhere in your system).   A number of recording in my collection sound the same both ways.  Most don't.  .
I have phase inversion switches on the rear of my Reflection Audio preamplifier and remote button for my Velodyne subs. With the subs off it's difficult to hear the differences of inverting the phase with most recordings partly because of the getting up to make the switch and my acoustic memory.

On the other hand changing the phase of the subwoofers extra low frequencies with the remote while remaining in the listening position the out of phase can be quite audible on recordings with forwardly mixed kick drums. In fact the phase can change from track to track. 
My speakers are inverted, judging by direction of woofer's membrane movement when small DC voltage is applied. My DAC and amp are non-inverting.  I switched wires and sound changed, becoming tighter in the bass.  It was also mentioned in few Stereophile reviews including this one (Dali MS5 paragraph):

I'm not sure why speaker designer decided to make it with inverted polarity, but I like it.  These speakers, in my room, sound better that way.  Of course it can be just the opposite for other CDs or it could be only my imagination - a placebo effect after reading Stereophile reviews, but I don't see a reason to change.

To complicate matters, the drivers in many loudspeakers are wired in various states of inverted polarity relative to one another. Vandersteen famously are not, all drivers in them being wired in the same polarity and crossed-over with 1st order filters, which maintains the speakers phase (at x/o frequencies at least). Many planars are of single-polarity design, of course. When you have speakers whose drivers are in opposite polarity to each other, good luck trying to correct for source material! I guess getting the midrange driver to move positively to a positive signal is the thing to prioritize.
bdp24, that might be the case in my speakers.  Somebody stated that midrange drivers are in the opposite phase to woofers.  It would explain why designer wired/marked woofers in opposite phase in order to preserve proper midrange polarity.