So lets say you suddenly got hit with a tail wind and increased your speed by 40 knots. To reduce the deviation slowly, how long are you talking, i.e., seconds, a minute or a number of minutes
The Airbus uses a different programme mode when in the cruise, to reduce the amount of thrust chasing (which is itself not efficient). So, in the cruise a variation of a few knots will be adjusted for, but not in any particular hurry. Probably around a minute or so. The system will become more aggressive as the deviation increases, and manoeuvring around weather at altitude it's not that unusual to see maximum power.
The sort of wind change you're taking about is normally seen in climbs or descents, and the response will generally be a pitch change, or manual selection of the speed brakes if that can't catch it. In climb/descent, the auto thrust isn't attempting to control the speed.
An instantaneous 40 knot tailwind at altitude would almost certainly drop your speed below Vmin drag, and you'd be unlikely to have enough power to accelerate again without trading off height. Thankfully not a normal scenario.
In level flight, a gust that puts you into the 'bricks', will initially be countered by thrust reduction (to idle if necessary), but if it stays above the max for more than a few seconds or about 4 (variable) knots the flight control system will cause a pitch up.
It's normally never an issue unless you're operating at the very fast end of the speed scale, and about .03 mach above the normal numbers.
On approach the systems are aggressive, and chase any speed change instantly.