Unneutered indoor cats go psycho (official medical term 
).
The hormones run riot in their bodies and, when they are unable to mate, begin to affect their brains. The effects normally start to show at around the age of four, but can vary immensely. It can cause all sorts of things, including weeing in strange places.
However even if that isn't causing it, leaving them unneutered will almost certainly lead to aggression, as well as a desperation to get out which will lead them to throw themselves out of tenth floor windows for example.
I work in cat rescue and one of my first ever jobs was to 'rescue' a woman from her unneutered, four year old female flat cat that had turned 'psycho'.
It was Summer, and a heatwave, and when I got there the woman was wearing boots, a full length coat, a hat and gloves, all to protect herself from the cat that was launching attacks on her. She said to me 'the cat's in there' pointing to her bedroom. I expected her to come in with me to help me catch it, but instead she opened the door, pushed me inside, and slammed the door behind me . I managed to catch when it attacked me and I lifted it up with its teeth clamped round my finger and sort of swung it into a top loading carrier.
After being neutered and given a few tranquilisers the cat reverted back to her sweet, loving self and went home.
That was the first incident but I've seen it many times since.
Anyway, so that's why they must be neutered. That may well help. Also, if they are just missing the tray then I would also try a hooded tray that they have to physically walk inside and so can't really miss. And for any other trays I would put puppy training pads underneath so that if they do miss it doesn't matter.
And you definitely need two trays.