It being Saturday, there is a risk of being a spoil-sport by returning to the OP's question.
Herewith some attempts at answering:
The 3-4 shift involves fluid flow to two operating elements (Band 2 release, and Klutch 2 apply) & and one accumulator.

So:

1) The output volume of the pump must be sufficient to supply these three simultaneously.
2) The working pressure (modulated) must not be too low.
3) The leakage past the seals of any or all of the three must be at a minimum.
4) The friction material of K2 (Klutch) must not be excessively worn.


The flair occurs when band B2 releases faster than clutch K2 applies.
A flair that persists causes rapid wear of the clutch friction material.