All the sources you mentioned are in fact correct, as there are a few parameters you need to provide when you ask such a question, with the most important being what type is your OnRep? Is it a C++ or a BP one?
The difference in those two environments stems from the fact that BP OnReps (known as RepNotifys) are in fact not replication callbacks at all. They are just a IPRopertyChangedTracker (in case you have access to C++) and that causes them to fire whenever the variable is set (no matter where), and that’s definitely not a replication callback (like OnReps are in C++).
The only source I’ve found reliable and covers all these nuances is this (which I keep referring to from time to time), which by the sounds of what you said, you should have come upon it, and it should have made things clear for you, not the reverse.
My advice is: Don’t do OnReps in BP unless you’re prototyping or that you don’t do C++ at all. BP RepNotifys are hacky, they will always be.