Spell Attack for Cantrips not of your tradition

This occured to me when reviewing the Kobold Sorcerer Grimmnir from the "Little Trouble in Big Absalom" Module.

As a Sorcerer of the demonic bloodline, Grimmnir is a spontaneous divine spellcaster. As indicated on p.191 Core Rulebook (2nd printing) he has these proficiencies regarding his spellcasting:

Trained in spell attack rolls of your spellcasting tradition, as indicated by your bloodline. Trained in spell DCs of your spellcasting tradition, as indicated by your bloodline

That gives Grimmnir a trained (+3) bonus to his Spell Attack Roll, as well as his key ability modifier CHA (+4), resulting in a +7. This is also indicated on his pregen character sheet.

Ranged [two-actions] acid splash +7 (cantrip), Damage 1d6 acid plus 1 splash

But when I looked up the Acid Splash Entry (p. 316 Core Rulebook (2nd printing)), it says Acid Splash is a cantrip of the arcane and primal tradition.

So:

  1. does he actually get only a +4 (key ability modifier 4 + untrained tradition 0) ?
  2. is he automatically trained in cantrips he earned from your bloodline
  3. are cantrips he earned from his bloodline automatically considered of the tradition he gained from his bloodline?
  4. does his spell attack work for for every spell he has, regardless of tradition?

1: would be… bad design for this bloodline? 2: you usually don’t use proficiency with a single spell. 3+4: would have the same outcome here, but could work differently if there are classes that actually gain proficiency in more than one tradition.