How does the A350 variable camber system decrease drag?
Henning Strüber, one of the Airbus engineers behind this system, has written a paper on it.

In cruise:


  This can be applied in early cruise phases to shift the center of lift more inboard and by that reducing the wing root bending moment, which can be transferred into a structural weight saving.


A plane that can be built lighter will have lower drag [for the same payload].

For a heavy and/or a hot and high takeoff:


  In high-lift configuration a more outboard loaded lift distribution can be achieved to reduce induced drag during take-off.


For how that works, see here. The answer there by @PeterKämpf confirms that outboard loading requires a heavy wing relative to the whole mass (scaling laws work for an insect, but not for an albatross or an airplane). So those two regimes may appear to be contradictory: if the cruise system allows a lighter wing, then how can that lighter wing achieve more outboard lift for a heavy takeoff.

Accounting for the gust loads in cruise is the key here, which are smaller for takeoffs. (Thanks to @PeterKämpf for this insight; see comment posted below.)