Yeah I have literally no idea if this is some kind of bug or something or maybe the game just tweaked the debuff quite a bit

As based on the description of the slowdown debuff , it strictly says that the affected units will start his/her action (whether it may be a standard attack or a mystery skill) at the end of the round, so essentially this debuff pretty much affects the lineup's "initiative status".
But what it doesn't indicate is that it also essentially affects the positioning of your lineup or rather the concept of who among the units will use the chase skill first in order to execute a good combo, stuff like that.

I kinda noticed this when i was using a team of gengetsu, azurefang, haku, and nagato on a team of crimson fist, kurotsochi,onoki, and asuma (windblade).
Kurotsochi used her mystery skill which affected the the team's initiative, except for nagato who was then at that time already immune to debuffs and ninjutsu.

The normal pattern for its combo when one uses knockdown is that it should be attacked by azure fang (summon) - gengetsu (chase) - azure fang (summon)- haku (chase) - azure fang (chase)- Nagato (chase) - Nagato (10x combo chase)
However, when the three units (azure, gengetsu, and haku) are under slowdown status , the combo only went like this azure fang (summon) - Nagato (chase) - Azure fang (summon)- Nagato (chase)

so yeah it essentially made Nagato as the temporary unit to be in postion 1, ruining the combo of the team