Assuming the Draytek is using 10.238.37.1 and the EX2200 is using 10.238.37.2, you need to install two static routes on the Draytek so it knows how to reach the 192.x subnets:
192.168.1.0/24 next-hop 10.238.37.2
192.168.2.0/24 next-hop 10.238.37.2
The ex2200 in turn needs a static default route pointing to the Draytek IP
set routing-options static route 0.0.0.0/0 next-hop 10.238.37.1
By default, yes.