[RPG] Does caster level always increase the number of scaling spells’ damage dice

Aether's answer certainly has good point, but I think you can argue his interpretation both ways (Fire Shield is an evocation spell that needs to be cast at some point and certainly can deal hitpoint damage, after all) since the ability doesn't explicitly mention that the spell needs to deal damage at the time of casting (this interpretation would also rule out some signature evocation spells like Delayed Blast Fireball from getting any benefits from this abiltiy).

I'd personally follow this line in the ability's description:

[...] This bonus only applies once to a spell, not once per missile or ray, and cannot be split between multiple missiles or rays. [...]

and allow the extra damage to be dealt once per casting of the spell (e.g. on the first hit, or on a single hit the caster decides). This would allow the character to still benefit from the class ability when using the spell but prevent it from being cheesed.

Your caster level (CL) is 8. Your maximum spell level is 4th. Fireball is a 3rd-level spell. Spells can be prepared in higher-level slots, although this does nothing special*. You can always cast a spell at a lower CL than normal**, down to the minimum CL needed to cast the spell for your class (in this case, 5th or 6th, depending on whether a Wizard or Sorcerer is casting it — presumably the former, given the mention of preparation). And fireball damage scales only with CL, per the original rules quote.

Therefore, you would cast fireball out of a 3rd-level slot for 8d6 damage normally, or as little as 5d6 damage at your option.

In two more class levels, your CL would be 10 and you would be casting fireball, still out of a 3rd-level slot, for up to 10d6 damage. After that, you don't get any more damage increases from the spell itself, although there are lots of feats and class features and what-not that can increase damage in various ways.

^{*Preparing in higher slots:}

^{A spellcaster always has the option to fill a higher-level spell slot with a lower-level spell.}

^{**Casting at lower CL:}

^{You can cast a spell at a lower caster level than normal, but the caster level you choose must be high enough for you to cast the spell in question, and all level-dependent features must be based on the same caster level.}