This article
is correct, though it sort of over-exaggerates the problem in a lot of more "normal" shooting situations. Unless you are using really big apertures and/or working in close with tele lenses, so that depth of field is particularly shallow, filed curvature should be mostly covered by DOF. Just watch out for too large apertures... one stop smaller might make a world of difference (and most modern camera viewfinders tend to make you think you have more DOF than you really do.)
Moving subjects or stationary? Which focus mode have you got set?
If you have time and the subject is stationary, it will generally be safest and most accurate to manually select a single AF point that covers the subject as close as possible to where you want them in the final image. Some post processing fine tuning crop might still be needed, but you can get close.
If shooting faster with stationary subjects, or photographing moving subjects, it may be best to select the center point (it's faster/more accurate on most Canon)... frame a little more loosely to allow room to crop in post.
With stationary subjects, One Shot is most accurate and once focus is achieved you can easily With moving subjects you need to use AI Servo, which normally doesn't allow for focus and recompose technique. If you also use Back Button Focus, you can do focus and recompose, but it will still be a problem due to subject movement. Best bet is to allow some room to crop later.
If using a zoom lens, most modern ones are varifocal designs. If part of your recomposing involves zooming the lens and changing focal length, you have to refocus the lens.