I figured it out.
For those of you who may later get the same issue, here is the config settings I put in the configure file:
domainlist smarthost_domains = domain1:domain2.com
In the routers section (the very first one):
driver = manualroute
domains = +smarthost_domains
transport = remote_smtp
route_list = +smarthost_domains IP_or_DNS_of_smarthost