To make sure that the area is properly cleaned, to remove any scents that might tempt them back, I would recommend using an enzymatic cleaner. I have used a product called Simple Solution in the past and found it worked well. It'll kill any residual smell and remove the scent markers they use for territory.
Falconsgyre is absolutely correct, that kind of correction is utterly meaningless after the fact. (and if your cat is doing it through pain or stress, then why upset them more if you catch them doing the behaviour you want to stop?)
Possible that the litter change is the problem. May I ask why you changed? I'm assuming the box(es) are still in the same place? Have you changed your cleaning routine or cleaning product?
Are you sure that it is more than one cat doing it? Sometimes cats avoid using the litter box because it hurts to pee and, in their mind, they are incorrectly associating the box with pain. I had a girl cat that got cystitis and I know that urinary infections can be an issue. Although I'm not so sure about that if it is more than one cat (unless it is catching - viral for example). Are you in a position to rule out any potential medical cause?
The cat you saw - was she spraying? (standing, shivering her tail) Or was she squatting? (the 4 girls I live with will all shiver their tail at stuff, but nothing that a human can discern comes out, no wetness and no smell, but it is possible for girls to piddle doing that).
Two more products that have worked for me in the past (and I don't work for a veterinary product store, I swear) are Feliway spray and Feliway plug in - the plug-in is like a room deodoriser, it fills the space with a pheromone that humans can't pick up but which will relax a cat that is doing territory marking out of stress. The direct spray is something you can specifically apply to locations they choose. I mostly use Feliway spray to stop clawing, but it has been known to work for piddling. You will pick up a mild scent for a moment or two, but I reckon that is the fluid the pheromones are suspended in and it will go away. Spot check it on fabric first.
