Yeah, that’s how it’s designed to work. The only times I’ve had my phone still notify is when the watch is on my wrist but locked, in which case both will buzz but the watch can’t display the notification. I’ve had an Apple Watch since 2016 and it’s always been like that.
It’s by design because, for most people, having both devices buzz would be redundant. You’re more likely to notice the watch since it’s on your wrist