Could this indicate that someone else is using the network, even though it's WPA/WPA2-PSK encrypted ?
Well, if you've chosen a stupidly easy WPA2 password then that could be.
However the more likely answer is DHCP.
The router runs a little server process which dishes out IP addresses automatically to devices that request it.
Most DHCP servers will lease the IP to a MAC address for a given lifetime, however it sounds like the DHCP lease time is set very short on your router and hence is why new IPs are being dished out.