What happened if I gained a +1 temporary bonus to ability score？

We just got a boon from Reign of Winter in PFS, but i'm not sure how this boon works.

(Assuming the Mantle): You have accepted the Mantle of the Black Rider, which grants you considerable power in your quest to find Baba Yaga so long as you continue your quest. Choose one ability score. Once per day as a swift action you may gain a +1 bonus to that ability score for 1 minute. For every additional Mantle of the Black Rider boon that you have for this character, the bonus increases by +1. You may not benefit from more than one Mantle of the Black Rider boon at a time.

It's obvious that the character can gain a +1 temporary bonuses on a specific ability score, but it seems useless according to the rule below

Some spells and abilities increase your ability scores. Ability score increases with a duration of 1 day or less give only temporary bonuses. For every two points of increase to a single ability, apply a +1 bonus to the skills and statistics listed with the relevant ability.

Then I found this FAQ of CRB, I think it means what CRB written is just something like "quick rules" for adding a simple template to a summoned monster, if you have enough time to prepare the stats you should use a "rebuild rules" instead. Both rules are legal and it's up to GM which one to take for the purpose of speeding up games.

For example, if a fighter has 19 str gain a +1 temporary bonuses on str, his str should be treated as 20, and if he has 20 str and get a ability score damage, penalty, or drain, the str is treated as 19. Am i right?

If not, how does this boon work in PFS?

Temporary Ability Score Increases vs. Permanent Ability Score Increases: Why do temporary bonuses only apply to some things?

Spoiler:

Temporary ability bonuses should apply to anything relating to that ability score, just as permanent ability score bonuses do. The section in the glossary was very tight on space and it was not possible to list every single ability score-related game effect that an ability score bones would affect.

The purpose of the temporary ability score ruling is to make it so you don't have to rebuild your character every time you get a bull's strength or similar spell; it just summarizes the most common game effects relative to that ability score.

For example, most of the time when you get bull's strength, you're using it for combat, so the glossary mentions Strength-based skill checks, melee attack rolls, Strength-based weapon damage rolls, CMB, and CMD. It doesn't call out melee attack rolls that use Dex instead of Str (such as when using Weapon Finesse) or situations where your applied Str bonus should be halved or multiplied (such as whith off-hand or two-handed weapons). You're usually not using the spell for a 1 min./level increase in your carrying capacity, so that isn't mentioned there, but the bonus should still apply to that, as well as to Strength checks to break down doors.

Think of it in the same way that a simple template has "quick rules" and "rebuild rules;" they're supposed to create monsters which are roughly equivalent in terms of stats, but the quick rules are a short cut that misses some details compared to using the rebuild rules. Likewise, the temporary ability score rule is intended as a short cut to speed up gameplay, not as the most precise way of applying the bonus.

A temporary ability score bonus should affect all of the same stats and rolls that a permanent ability score bonus does.

I'd suggest applying the rule "A temporary ability score bonus should affect all of the same stats and rolls that a permanent ability score bonus does."

I've always run it as the score is treated as if it were a 20 for all purposes except feat prerequisites. Otherwise you get weird exceptions on two handed weapons.