People often imprecisely say that type of regulation takes place on the order of many minutes to hours, and that may be as precise as you can get given the variable kinetics of any given pathway.
Also, all genes in eukaryotes require general transcription factors, but basically all of them also require activators to act first to recruit the GTFs and histone modifying components (which allow GTFs and their friend RNA polymerase to access genes). So, they are generally downstream of activators and their recruitment is part of what contributes to the kinetics in euakryotes.
For RNAi, the kinetics of knockdown in RNAi could largely depend on the rate of degradation of the protein (which is HIGHLY variable). Even if you take away the mRNA, the protein is still there until it's degraded. If it's normally degraded fast, the kinetics of mRNA degradation will be limiting. If it's slow, then you have to wait for the protein to be degraded by its natural mechanisms (https://en.wikipedia.org/wiki/Proteasome).
Sigma is saying RNAi effects can be seen in around 24 hours
Thermo is implying something similar by saying RNAi effects can be seen for 5-7 days post-transfection (i.e. they imply that it can be seen after a day).