Sam, as I recall, the usual time to add herbs and spices is after draining the curd but before pressing. Otherwise, you'd lose most of the flavor when the whey drains away. I'm sure there are exceptions; for example, I think I remember seeing some "threads" where saffron "threads" were added directly to the milk. (I'd say, "no pun intended," but no one would believe me!)
Personally, I'd want to be very sure the oils are food-safe and sterile - not just free of bacteria, but free of any mold spores. When you work with herbs or spices, the way you usually do that is to boil them in some distilled or filtered water; strain the water into the milk (and yes, most of this flavor will be lost in the whey, but might as well); then add the cooled herbs to the curds and mix them in before pressing.
I know many folks here do this (adding cumin to Gouda or peppers to Jack, for example), but I confess that I have always been a little hesitant - visions of botulism dance in my head. I'm sure that there is a reason this isn't a concern, since it is so commonly done, but ... I haven't yet done the research to convince myself.
So all of the above is based on my memory of what I have read ... aka, take it with a grain of salt!