To add mods to your Terraria server, you must first be running tModloader. If you haven't already, contact support to convert your base Terraria server to a tModloader server.
Once your server is a tModloader server, gather all your mods' workshop IDs
Once you have all your workshop IDs, place them in your Startup tab's Workshop Mod IDs box so that the server will automatically fetch the latest versions and automatically update them