Is it common for scary sightings to stop as you get older?

It can happen. Kids can have intense nightmares and vivid impressions around bedtime or while waking, and shadows or ordinary room sounds can feel much scarier in the dark. Those experiences may become less frequent as sleep patterns, fears, and the way someone interprets things change with age. That doesn't tell us exactly what caused any particular memory, but it isn't automatically evidence of anything paranormal.

I'd look at the timing first. Experiences just as someone is falling asleep or waking up can be especially vivid, and sleep paralysis can include a strong sense that someone is nearby. Changes in a room, lighting, noise, stress, or sleep can also affect what someone thinks they saw or heard. Moving house and then noticing the experiences stopped doesn't by itself show that the old place had a supernatural cause.

If it's only an old childhood memory and it isn't causing trouble now, there's usually no need to treat it as an emergency. If frightening sights or voices are happening repeatedly while fully awake, disrupting sleep or daily life, or making someone feel unsafe, talking with a doctor or mental health professional would be a sensible next step. They can help sort out possible sleep, health, or stress-related explanations without dismissing the fear.