How does a router know which client to route an incoming packet to when it it performing NAT?

I’m an IT professional with a working knowledge of networks, but I just realized that I don’t fully understand NAT. Here’s a purely hypothetical question.

If two devices on a multi-client LAN with one WAN IP send out a request for reddit.com and both currently have open TCP connections with the same IP address, how do they accurately receive different responses? Would the Reddit server somehow include the client’s internal IP in the response for the router to read when it decapsulates the packet?