Hiya,
Cockers can tend to be rather dramatic in their telling off, is he a working cocker, their patience threshold is not as a rule the highest. Personally for me if he's making contact then he's taking things to far as it's easy ofr an accident when they are being over dramatic and if the pup moves quickly then she could be marked.
If pup was worried about the telling off, she wouldn't be repeating the behaviour that got her the tellling of in the first place Maybe, maybe not, pups are impulsive and act a such without relly thinking things through, and there is always the possibbility that repeated episodes of this could ruin her confidence - I've seen it lots of times. Cockers can be very good a becoming a bit bullyish and that really isn't a pattern that you want to develop. Yes another dog telling a pup off for being in their face is fine but there are limits and making contract for me is over that limit - your cocker needs to learn some self control as well as the pup. It also depends on the age of the pup and what phase they are going through devlopmentally, an overreaction from another dog at a fear impact stage could have a much bigger effect!
What I would do, rather than thinking of correcting him, is try and avoid the pup encroaching too much in his space for the time being, maybe with the use of a house line, so that if you can see your cocker is getting close to reacting or she is taking things too far then you can ask her to 'leave' or tell her 'enough' and then encourage her away with the use of the line and then rewardher for coming away from you. I think to a big extent it is our responsibility to teach our dogs what we want from them rather than leave it to our other dogs and also your cocker opbviously isn't comfortable with that close contact yet so best to let them get to know each other slowly.
I would also very carefully build up positive association with the pup for the cocker, so maybe pop your cocker in a seperate room to your other two and then bring in the pup into the same room as the cocker and fed them both high value rewards (if needs be tiw the pup up to something so they both have enough space), something like roast chicken, then when you stop feeding them take the pup out. Gradually get them nearer each other, this way the cocker caan build up a really positive association with the pup. This is just one example there are lots of way of building positive associations for them but it does need to be specific.
If the cocker does get to the point of realkly over reacting to the pup, which I would try and manage so it doesn't happen for the time being then I would pop him out the room, quietly and immediately and give him a few minutes to calm down.
Puppies usually have something called puppy lisence for a reason - they need time to find their feet and build up confidence, yopur other dogs will start being firmer in their tellings off when he gets a bit older but at the moment the pups experiences withother dogs for the main should be positive ones. Including meeting other dogs than you own

Hope that makes sense.