Phugoid is too long period a motion, typically it's measured in minutes, this was over in a minute or so it seems.
Not sure I completely agree with that. In the simple approximation the phugoid period is sqrt(2)*pi*v/g. So at 135 m/s (about 270 KTAS) the period is about 60 seconds. I'm not suggesting the aircraft went through an entire cycle, just a quarter cycle.
The traces in PickyPerkins's post look mostly like phugoid motion, don't they? If you picture the airspeed at 11:50 as an equilibrium value, a sudden increase with a maximum at about 12:00 leaves the aircraft with excess lift. What follows is broadly, constant AOA, with altitude increasing, airspeed decreasing 180 degrees out of phase, pitch attitude leading the altitude by 90 degrees. Thus it looks like the phugoid will have gone through a half cycle by about 12:25.
However, it looks like the crew intervenes at just after 12:20 with a great big downward punt on the controls, pushing the nose, and therefore AOA, down by 15 degrees. And they did that at just the wrong time, because the nose is about to go back down of its own accord, so instead of halting the oscillation, they exacerbate it.
Of course, since the modes are coupled, it's more complicated than that, but that looks like the broad idea.
How do the numbers work? An airspeed excursion from 325 KTAS to 365 KTAS (250 KIAS to 280 KIAS) is "worth" a bit less than 1200 ft of energy. It looks like the amplitude of the excursion was rather more than that, but that may be disguised by the aircraft being in a climb to start with. Or it may be that the airspeed started below 250 KIAS -- we don't know what went on before 11:50.