DNAT translates only the destination address of the packet. As you've discovered, the source address will remain the same when using a DNAT rule. Rather than translating all addresses with the SNAT rule, you may see benefit in translating only specific IPs in the SNAT source.
If your experience is with Cisco networking, you are probably used to a single static NAT statement performing the translation of the external address to the internal address on inbound traffic, as well as implicitly translating the inside address to the outside address on the way out.
A good article on NAT: NSX-V Edge NAT | VMware Professional Services