You're right. If it's a bigger quantity (say, more than a spoonful), then "schütten" would be the right verb: "den Reis/die Linsen/das Gemüse in den Topf schütten"
For smaller quantities: "hinzufügen" (to add to; written German), "reintun" (to add, informal)
And yes, I know, verbs, especially with their prefixes, are a real bother in German - sorry ;)