it should work rods are one handed weapons after all but I wouldnt be suprised if those doctrines are meant for melees or if they're not working at all. if I remember correctly witchfire was heat damage so you can try heat damage boosting doctrines.

damage type is whats important. if you want to buff specifically witchfire's damage go heat. damage type is written right next to dps. warpheat is just your resource it doesnt effect anything other then is anomalies going to bite you in the ass or not.

The answer to your question is in the description "One-Handed Melee Weapon Skills" a rod is first of all not a melee weapon but a ranged weapon. Second thing, it deals heat damage so Phosphoenic Psalm + Binharic Psalm + Volkite Psalm + Terminus Psalm+100% Heat Damage is the correct psalm code doctrine. You just have to look at ability tooltip. All the tags are in there and if you see an ability or anything else referring to that tag it means that it works with it.