The study you refer to Ivo is Dujic et al. 2009 from Croatia (1). They looked at dry static apnea. Diaphragmatic contractions began after 2 or 3 minutes, and increased in frequency. Negative pressure spikes in the chest increase venous return of blood to the heart and thereby increase stroke volume. There was no change in peripheral vascular resistance, so the increased cardiac output largely goes to the brain. It is like reverse CPR that pulls extra blood into the chest every few seconds.
It would be difficult to do a control study in the absence of contractions to see if contractions actually prolong BH time, since this would require paralyzing the diaphragm and chest muscles. However, contractions probably do buy a little extra time by raising brain O2 levels during the middle and later stages of apnea. This would be true only if apnea time is limited by hypoxic black out. It would not be expected to affect CO2 levels significantly, so the effect on urge-related breakpoint is not so clear. But as discussed in the SciAm article, breakpoint may be further prolonged by the mechanical effect alone of diaphragm movement. It should be pointed out that there was no facial immersion or cold stimulus in this study, and hence no diving response.
It’s not so clear what role contractions might play during a dive because there are many other factors involved, such as different lung volumes, blood shift, diving response, hyperbaric gas levels, etc. But the same effect likely does happen, and one would expect a small increase in cerebral blood flow due to contractions. Again, this would presumably be beneficial only if the diver is close to hypoxic black out. The time gained however might be offset by the increased oxygen cost of muscle contraction.
(1) Dujic Z, Uglesic L, Breskovic T, Valic Z, Heusser K, Marinovic J, Ljubkovic M, Palada I. Involuntary breathing movements improve cerebral oxygenation during apnea struggle phase in elite divers. J Appl Physiol. 2009 Dec;107(6):1840-6.