How should one reprimand a cat that has done something wrong before you saw it happen, so you don't know when it happened?

Correcting or reprimanding a pet is called positive punishment because the stimulus is aversive and added. Positive reinforcement is when you add in a rewarding stimulus. Negative punishment is when you take away a rewarding stimulus and negative reinforcement is when you take away an aversive sitmulus.   For positive punishment (reprimand) to work it must be consistently applied, immediate, and always clearly related to the bad behavior. There has to be certainty that jumping on the counter, for example, will evoke a reprimand. I doubt you are there 24/7, so I don't think you can make this work without putting an electric fence on your countertop. I try to never reprimand animals. I prefer a version of training where you always set them up for success, where they cannot fail. They may need to work outa problem, but they will succeed. So, if you have problems with a cat jumping on the counter and getting into interesting things, remove the interesting things, and then the cat will no longer be rewarded for jumping on the counter. It may still jump up, but it won't get on your nerves anymore.   If your cats are bored, you can try doing training exercises with them. Look into clicker training--there are good tutorials on the web, and tons of good books on the subject. Sometimes just giving them something to do that is more rewarding than being bad is enough to extinguish the bad behavior. Wouldn't you prefer if your cat came up to you and wanted to play rather than pushing things off of a bookshelf to see what they sound like when they fall? Me too.

Don't.  It's pointless and harmful to even try.  Cats will only associate a correction with something they've just done (or are currently doing) if it's immediate. Once the cat's attention has turned to some other activity, any correction will be associated with that activity and will only confuse and alienate the cat by appearing to be random hostility. If you can't give an immediate correction (and give it almost every single time the cat engages in the undesired behaviour — consistency is everything and inconsistent correction can perversely reinforce the behaviour), remove the temptation for the behaviour if that's practicable. If the cat repeatedly pees on something that is lying on the floor, remove it (and check the litter box; the problem is likely to be there).  If it persistently digs in a plant pot, cover the plant pot or move the plant to a cat-inaccessible location.

There is no 'right' or 'wrong' in the animal kingdom. There are only instincts and training. Undesired behavior should be corrected by re-training, and by giving the pet more desirable options.  (Yes, it is usually long and tedious, but the only fair way for the animal who is just being him/her self.)

It usually doesn't help to reprimand them after the fact. If you catch them in the act, gently grabbing your cat by the scruff of the neck and giving it a slight side to side shake, mimics how mothers reprimand their kittens. Just remember your goal is to communicate with your pet, not hurt him or her.