Public punishment reasserted the sovereign's momentarily injured authority. [causal]
The Pasha is saying that he takes these offenses very seriously because he considers them an attack on his sovereign person. It is his “momentarily injured sovereignty” that had to be avenged and the public punishment was seen as a way of reconstituting this sovereignty.
Builds on: "Corporal punishment signified the Sovereign's personal authority, not cruelty."
Khaled Fahmy, All the Pasha_s Men_ Mehmed…, loc. 675