Technically correct advice since increase in wind speed tends to move the apparent wind direction forward ( a "header") but in practice I prefer to head up as you do, keeping her "on her feet" is faster than excessive heel.
Edit: Wait, i was flat wrong above. the puff will seem like a Lift since your existing forward speed won't pull it forward as much as it did the pre-gust wind. So the apparent wind vector initially moves aft, a lift. (then, as you accellerate, you pull the apparent wind forward so you can bear off a little after the initial head-up, and then bear off more as the wind eases but your boatspeed is still higher from the puff.
I knew there was a reason I said I initially headed up ;-)
All this assumes the gust has the exact same compass direction as the breeze just before it. Which ain't always so, gusts can "spread out" so direction can vary quite a bit. The best sailors can read the water and make an educated guess.
PS I'm talking dinghies and hotrod boats here, heavier ones may not alter quick enough to conform to a quick apparent wind direction change.
PPS I may be over-complicating the whole thing. Yeah, head up initally, discretion is the better part of valor....