They are correct.
Teysa Karlov won't copy activated abilities. To tell the difference between activated and triggered abilities ...
An activated ability is written as "cost:effect". There is pretty much always a colon in an activated ability. In the cases of Priest and Whisper, the cost includes the tap symbol and sacrificing creatures. An activated ability is something that the player chooses when to activate and pay the cost.
A triggered ability typically begins with the words "When" or "Whenever". Something like "When this creature dies" or "Whenever a creature you control dies". There typically is no cost associated with a triggered ability. It is something that will happen whenever the condition is met whether you want it to or not.
Blood Artist and
Black Market are examples of triggered abilities that
Teysa Karlov will double.
Happy Brewing!