Overall MVesseur, it was a wonderful review. People need to know that all-in-ones have issues with CA. But they also need to know why the CA exists and how to resolve it.
Noting Chromatic Aberration ("CA" or Purple Fringe) is important about a lens review. A lens that is designated as APO or Tamron's XP, means that even in the lowest Aperature (F-Stop) settings, there is very little CA.
While compact telephoto lenses, "All-in-ones," and cheap 70-300s are all prone to low aperture CA; switching to a higher F-Stop (around F10-20) will generally eliminate most or all fringing issues in these styles of lenses.
CA/Fringing has nothing to do with brand, but rather the style or construction of the lens. I recommend that anyone who has a lens of this sort to try the aforementioned technique.
According to reviews, the Sigma 70-300mm APO is an amazing lens, but should not be compared to an "all-in-one zoom" style 18-250mm, because it's convenient ability to 'zoom out' that creates CA at low aperture. Something has to give, image range or image quality.
To be fair and honest, I only use APO and XP lenses right now, though I have had 'normal' lenses in the past. In a 'normal' lens, raising the F-stop does the trick nearly every time. One should never be used at full zoom with it's lowest aperture, this is why raising it to between F10-20 resolves the issue. But that is why some (like you and I) spend extra money for additional lenses or ones that can be used 'wide open,' and not have to sacrifice light in order to get that great zoomed shot!
Congratulations on your new 70-300 APO purchase! I would like to try one out sometime...