Righteous Fire and support gems are making my brain hurt. Help Please!

I decided to really try a righteous fire build for the first time, but I am running into issues that are just not making sense to me. I will do my best to say what I think is or is not happening and maybe someone somewhere can tell me what I am getting wrong, hopefully.

Please bear in mind that my gems are not +20 quality and hopefully my screenshot links will work so whoever looks can see what I am talking about.

First is a screenshot of the character screen showing the righteous fire offense tab as well as the empty links for the support gems:

https://prnt.sc/hxmzgm

Next I add the first support gem and the dps changes as it should:

https://prnt.sc/hxn0rc

Now I add the second support gem and again, the dps changes:

https://prnt.sc/hxn1k9

Now here is where everything goes crazy. The Chance to Ignite gem as well as the Immolate gem do not work as the Elemental Focus gem states "Supported skills cannot inflict Elemental Ailments." They in fact work exactly as intended.

But.....
when I add Controlled Destruction there is no dps change even though righteous fire is a spell skill that deals damage:

https://prnt.sc/hxn4fw

When I add Increased Area of Effect, the area changes as it should, with no increase to dps:

https://prnt.sc/hxn5d9

But when I switch to Concentrated Effect, the area shrinks as it should, but there is no dps increase:

https://prnt.sc/hxn6cl

Am I completely wrong in my understanding of how these support gems should be working, or is there an issue with the righteous fire offense tab? Or am I just going crazy?

Righteous fire does not do spell damage so spell damage modifiers won't help it. Tooltips are often not entirely accurate. There are righteous fire damage calculators you could use to help you.

That doesn't make sense. Righteous Fire is listed as "Spell, AoE, Fire". Also Efficacy Support increases the dps based on the "Supported Skills deal **% more spell damage." Also Concentrated Effect is listed as "Support, AoE" and it says "Supported skills deal **% more area damage, Supported skills have **% less area of effect." Even if its not based on spell damage, then Concentrated Effect should still increase the overall dps.

APPARENTLY (even though this makes no godsdamned sense) Controlled Destruction doesn't work because Righteous Fire doesn't deal damage - it grants you a buff that just-so-happens to deal AoE Fire (but not spell) damage to nearby enemies. Yeah. Sometimes Path of Exile makes my brain bleed.

Anyways.

Chance to Ignite 'works' in that it increases the Fire damage the skill does, but the Ignite chance is moot since Righteous Fire doesn't hit and thus can't ignite.

Immolate (supporting Righteous Fire itself) is a no-go - you need to hit for Immolate to proc, RF can't hit, and so Immolate does nothing. Immolate supporting a hitty skill targeting something within the AoE of Righteous Fire (such as Flame Surge)? Absolutely, it's an excellent combo.

Elemental Focus is a free damage boost. Again, you need to hit in order to apply elemental status effects, RF doesn't hit, and so RF can't apply elemental status effects anyways.

Conc. Effect should be working, as RF is area damage and area damage scaling in the tree works for it. Unless it's another weird nonsensical interaction like Controlled Destruction.

What you're missing (I think, I can't tell what's going on in your screenshots) is Burning Damage Support. That's the big one for Righteous Fire builds. Also Scorching Ray builds. Or builds that do both, which are increasingly common. Righteous Fire and Scorching Ray combo together exceptionally well, you may want to consider it.

Burning Damage support does not increase the listed dps. Are the screenshot links not working?

RF does not "hit", so it cannot ignite anyway. Although RF is a spell, its damage is a "de-buff" not spell damage.

Elemental focus, Increased Burning damage, and Concentrated Effect are the best supports for RF.

There are others that can have lesser effect. I think Efficacy works.

The next best thing is to have as much life as possible, and enough fire resist (85% is achievable without flasks) and life regen to handle it.

Secondary damage boosters are - Flammability / Ele Weakness curses
- Scorching Ray
- Elemental Equilibrium

I used an RF Chieftain in SSF harbinger, Arc with Flammability on hit, applied the curse and triggered EE, and i threw down a scorching ray totem for bosses and tough rares.

Made it to level 90 and walked through T10/T11 maps with zero effort.

Well, I am going to try the ones you listed even though the offense tab dps is lower than before. I already was using Scorching Ray but I switched from decoy totem to searing bond so I will see if this affects the overall dps. Thanks for the help :)

Don't bother putting Scorching Ray on a totem. Just cast it yourself; that way you get Searing Bond, Scorching Ray, and Righteous Fire all three. If you want to do the thing where you deal damage without stopping to cast, just leave off Scorching Ray for a while.

Heh, also invest in Aberrath's Hooves so you can do fiery explodey hits while you walk. Layer on ALL the passive damage!

go and read a few guides on RF/SR. Those would have helped you the most.
PoE is complex and not very intuitive.