This is actually not completely true. The partial pressures of the gases remain to great extent uninfluenced by the exhale. There is no reason for them to change when you exhale.
The partial alveolar pressure of oxygen is determined by two main factors: 1) the absolute pressure of gas in lungs, and 2) the ratio of the part of oxygen to the total volume.
1) The pressure in lungs is only dependent on the ambient water pressure, and is equal to the ambient pressure on inhale as well as on exhale, hence no change here. There may be a very slight overpressure due to extreme packing just on surface, or perhaps still a feet or two under it, but definitely no anywhere deeper. The overpressure may be accentuated by the progressed bloodshift on ascent, but in the same time reduced due to the loss of gas volume due to oxygen consumption (the CO2 production is slightly lower). But still, any excess overpressure concerns only the very last feet or two, hence the impact of exhaling on PaO2 during the ascent is inexisting.
2) By exhaling you do not change the ratio of O2 in lungs (at least not in short term). You cannot exhale oxygen without exhaling also the other gases in lungs, hence the percentage of oxygen after the exhale remains practically identical to the level before it.
So, as you see, there is no way the PaO2 could change, and strengthen so the "vacuum effect" due to exhale, as is often incorrectly claimed in freediving courses, or even in some books.
That told, when remaining longer time with considerably lower volume of gas in lungs, the gradient of oxygen intake from this remaining volume has proportionally stronger effect, so when the exhale is done a long time before surfacing, it could indeeed contribute to quicker drop of PaO2. There is though no such risk when done on the last few meters.
From this point of view the exhale at 20m as Eric tells, is surprising to me too, since it is still rather deep; but I guess he relies on strengthening the Diving Response, and perhaps uses it also for buoyancy control to slow down the last phase of the ascent (reducing so the risk of DCS). He will certainly tell us more.
A good reply as usual Trux, but in the end I think you agree with me and the text books?
"That told, when remaining longer time with considerably lower volume of gas in lungs, the gradient of oxygen intake from this remaining volume has proportionally stronger effect, so when the exhale is done a long time before surfacing, it could indeeed contribute to quicker drop of PaO2. There is though no such risk when done on the last few meters."
I would sum up, in my lay level, that at the critical last 10M every drop of 02 helps (and the higher blood pressure too as was well mentioned above), and any pressure drop (exhale) is not good if you are on the edge.
As I stated, this can be experimented with in competition scenarios with good safety. But, to think of badly watched spearo's trying the same ideas (that they may read here) would IMHO be very bad idea. I would therefore generally endorse the recommendation: don't exhale before the surface.