roulis
A real dutch roll is an OSCILLATION from one side to another with increasing bank due to resonance.
Despite you have a yaw movement in the dutch roll, the names says it well it s a ROLL oscillation, to be corrected with the stick not with pedals.
Dutch roll is certainly an oscillation, but it doesn't
have to be one of increasing bank; in fact it would be a lousy aircraft for which that were true - very probably unflyable. Increasing bank as a result of suitably (mis)timed pilot inputs is quite another thing.
Sure the rolling motion is usually the most obvious sign of a dutch roll, but the motion is a combination of two oscillations - one around the roll axis and the other around the yaw - linked together by a common driver - sideslip.
Way back in the 1950s Ashkenas and McRuer established the importance of the roll/sideslip ratio as a parameter to describe the goodness/badness of dutch roll. The larger the number the worse the aircraft basically. So dutch roll can be triggered by rudder application, but as you say it is best controlled by aileron.
So far as I know, the A300 was not noted as having poor dutch roll characteristics.