Unsure what they mean precisely, But I'd guess to not decrease the drop too much from a pair to the next. Take all I say with a huge grain of salt as I'm by no means an expert on biomechanics (or even running shoes), but I'd think that alternating from a day to the next between very different shoes could prove problematic. I think your overall running gait (how the feet attack the ground, how the muscles exert efforts) can change pretty drastically with different sole shapes. I know it took me some time to adapt before becoming comfortable. I'd think your legs might "get confused" so to speak if you keep switching back and forth, if that makes any sense. So I'd think moving towards a pair with slightly lower drop, possibly taking it easy for the first cple of weeks of use (especially if feeling soreness), and paying attention to your form (e.g. avoiding heel strike) would overall make sense.
I honestly don't feel much of a difference due to limited padding. I don't run all that much, but a lot of it has been on hard surface (streets, pavement). I don't feel any particular soreness or stiffness. I used to get shin splints and pretty bad back soreness a while ago when running on thicker, cushier soles. But that could honestly have been due to all sorts of factors and not just the shoes (I was much heavier back then). That being said, I don't feel the lack of padding has been a problem, but we're obviously all different, ymmv etc.
When I swapped to lower drop shoes (which btw was by accident and not by design, I needed new shoes and bought what felt most comfortable on my feet in the store, not knowing or noticing the difference in drop), the third or fourth time out with them I started feeling sharp muscular pains on the hip, upper thigh region, just below the joint to the collarbone, on the outside. It showed up after about 20mins of efforts and was sharp enough I would have to slow down. It would recede after slowing down to a casual pace for a few minutes but would come back if I picked the pace back up again. It gradually went away after a few weeks.
Edit: hmmm, actually went over the last 13 months from nike lunarlon (10mm drop) to nike flex (4.5mm) to nike free (8mm?). Pains and gait adjustment occurred in the tansition from lunar to flex (10 to 4.5mm). I just recently switched over to the free, but I didnt feel much of a difference if any, had not realized I had gone back up to 8mm.