How exactly does Burn It! (and similar effects) affect splash and ongoing damage?

The level 1 goblin feat Burn It! gives a status damage bonus to all spells and alchemical items that deal fire damage. It also gives a status damage bonus of +1 to all ongoing fire effects. How does that work with splash damage?

For example, suppose I’m a low-level goblin with the Burn It! feat, who really, really likes fire, and who has just come into a bit of money. I decide to blow it on an alchemist’s Fire (Greater). It’s got +2 to hit, and deals 3d8 fire damage, 3 persistent fire damage, and 3 fire splash damage. It’s level 11, and Burn It! gives a bonus of a quarter of that (min 1) to base and splash damage. I spot two people I don’t like standing next to each other, pitch it at one of them, and hit. Now, without the feat, it’s pretty simple. The guy I hit takes 3d8+3 (base plus splash) and 3 ongoing. The guy next to him just takes 3 splash. With the feat… what happens? Does it affect the splash damage at all? If it does affect the splash damage, do I get the bonus twice on the main guy because I hit him with both base and splash? Does the ongoing damage get just +1 (for being ongoing fire damage) or the full bonus (for being fire damage from an alchemical device)? How is the actual bonus determined (given that the level is not evenly divisible by 4)?

there is a question that covers part of this from the playtest, but it appears that at least some of the rules text has changed since it was written, and it doesn’t cover the full thing.