There's almost no wrong way or time to add hops to a beer...all have subtle differences in the results.
Flameout Additions: Adding hops at flameout drop them in at a moment when the wort is still boiling (it SHOULD be anyway, right up until flameout) for the last few minutes as the temperature starts to decrease. Although alpha acid utilization is practically nonexistent without a solid boil according to the calculations, through a mechanism not entirely understood, the flameout additions DO add a fair amount of IBUs, although at a much lower rate than usual additions. By increasing the hop bill dramatically, brewers are using a technique called Hopbursting - adding ALL of their hops at flameout. The result is a smoother bitterness with massive flavor and aroma qualities. By adding while heat is high, risk of grassy and vegetal hints are reduced.
Hot Hopback Additions: With a hopback, the hot wort is drained or (more likely) pumped through a chamber with a compressed mass of hops. The wort spends relatively little time in the chamber, but the pressure forces rapid pickup from the hops. Hopbacks don't generally work well with pellet hops. Hot additions work much like flameout or early whirlpool additions, depending on the temperature of the wort as it passes through the chamber. The main difference is that your wort is moving at higher pressure through hops that are more compressed.
Whirlpool Additions: Adding hops after cooling has begun or after chilling is complete can vary a bit, depending on the warmth of the wort when the hops are added. The hops are able to circulate freely and loose throughout the volume of the wort and are then collected with the break and other debris before separation/transfer to the fermenter. Adds a hint of bitterness, a bit of flavor, and a huge aroma burst. If hops are not of quality, there can be hints of parboiled vegetals that can be unpleasant.
Cold Hopback Additions: With a hopback, the chilled wort is drained or (more likely) pumped through a chamber with a compressed mass of hops. The wort spends relatively little time in the chamber, but the pressure forces rapid pickup from the hops. Hopbacks don't generally work well with pellet hops. Cold additions add significant aromas, and maybe a little flavor, but usually little else. Be careful with your quality of hops, as old, wilted or bruised hops can convey grassy, vegetal tones.
