Unless it's raw milk cheese, the milk is pasteurised, then cultures are added. Calling it "cultured milk" isn't something I'd personally ever do on a label but I'd see it as the same thing as "pasteurised milk + cultures".
I read the spec and label and thought "those read the same thing". I'd personally not appreciate them not specifying they were sometimes using beta carotene and sometimes annatto and that should be clear on the spec in my view or at least both present if they're spot buying and it may contain either.
The attitude isn't great to be honest, I'd have expected them to be a bit more kind in their tone and explained that they are essentially the same and even apologise because while they mean the same thing, they should be consistent.
You do have some odd questions sometimes with dairy though and dairy companies often supply everybody. B2B and retailer meaning writing specs, labels etc is just massive workload. So when you get what you might perceive to be a daft question, perhaps you just got them on a bad day when the list of questions from other customers was huge. Not an excuse but just explaining.
Some of my favourites when I worked in dairy were complaining that cheddar was arriving at too high a temperature, when it was arriving straight from maturation storage and the customer didn't understand maturation isn't at 5oC and kept trying to insist our specs should say this. The questions only stopped when the sales team got involved to explain adding a blast chilling step would delay orders and add cost.
Another was that they didn't want any rennet which had been made from microbes using GM technology.
"Ok, so you want animal rennet?"
"No, we still want vegetarian rennet."
"Ok. This is how they make vegetarian rennet... it doesn't mean any GM material is in the final product, the GM microbe produces the rennet then it's purified."
"My other supplier can supply vegetarian cheese without using that rennet!"
"Ok, you go back to them and ask them how it's produced, then come back to me with their answer."
No reply.
There's never an excuse for rudeness. But I'd just jot their attitude up to experience if I'm honest. Not that it's nice. I think it's just frazzled people who respond rudely sometimes. Or they're utter idiots who won't feel bad anyway so there's no point.