Sorry, I missed that you also needed to initiate traffic outbound from the server. The setup so far only takes care of inbound traffic to the server.
For the outbound traffic it uses the other interface due to the routing setup of the device. You will need to add source based routing that will take any connection from this internal ip address source and use the second ISP ignoring the outbound destination route table.
https://kb.juniper.net/InfoCenter/index?page=content&id=KB4273
Once this is setup you then need to add an outbound policy with source nat.
Create a dip for the public address
Use this as the source nat in the outbound policy advanced tab