All the hydraulic systems have multiple accumulators to smooth out the pressure delivery. Accumulators also assist the main pumps by supplementing the system pressure when a large demand is made - such as the landing gear being moved.
If the accumulators are leaky, or not charged with the correct nitrogen pressure, the Green Hyd pressure might well momentarily drop below the PTU triggering pressure during gear movement, or indeed multiple demands, so it cuts in briefly to help.
In the cabin one can certainly hear the PTU blipping on very briefly in some aircraft during gear deployment. I don't think one or two second's operation is long enough for an ECAM memo to be triggered though?