I've seen a 13 week old pullet willingly squat for a 13 week old cockerel. They went through the entire mating routine, including touching vents. That pullet did not start laying for another two months. A pullet squatting does not mean she is ready to lay.
The mating routine with adolescents is much more about dominance than it is about sex. The one on bottom is accepting the dominance of the one on top, either willingly or by force. It sounds like your pullet accepts the dominance of that cockerel. An adolescent cockerel looks like a sex crazed maniac but he's not really. The hormones are more pushing him to be dominant than just going after sex. He can enforce his dominance by fighting if they fight back. If they don't fight back he may chase and peck. Or he may force them to mate with him on top.
It's fairly rare but occasionally a cockerel will mount another cockerel. That doesn't mean he is weird, it means he is dominant. Occasionally, especially if no mature rooster or somewhat mature cockerel is in the flock, you will see a hen or pullet mounting another female. That doesn't mean she is weird, it means she is dominant.
I suggest you get the nests installed and opened now with a fake egg in them. I have seen pullets start to lay by 16 weeks. I expect some have had them start even earlier. Often before they start to lay a pullet looks for a suitable nest to lay her eggs, often as much as a week in advance. I want mine to learn to lay in the nests instead of somewhere else. Not all pullets do that, egg laying seems to catch some by surprise. Those can drop an egg anywhere, from the roosts at night or just walking around. But at some point they will look for a nest to lay in. I want my nests to be in consideration.
Another reason I want the nests open before they start to lay is that if I am going to have problems I want to know about them before I have broken or poopy eggs. Part of that nest search usually involves scratching. If your nesting material or fake eggs end up on the coop floor it probably means you need to raise the lip on the nest.
Occasionally chickens will sleep in the nests instead of on the roosts. If your roosts are noticeably higher than the nests this usually doesn't happen but it still can. If they are sleeping in the nests instead of the roosts there is usually a reason. Chickens poop a lot at night. If they are going to sleep in the nests I want to solve that problem before I start to get poopy eggs.