It's long been standard practice with tantalum filter capacitors to feed them through an inductor or at least a resistor to prevent inrush current failures. That, and/or you derate the crap out of them when you design the board. Newer drives are probably using multilayer ceramics that can put up with just about any abuse including inrush.

Executive summary: powerup stress is not an issue unless the drive was designed by a moron.