Good question, makes sense - anyone have any official rules reference for this? It's easy to implement and might make this default even if no official ruling. Thoughts?
I believe the official ruling (no citation though) is that a class does not count as a caster until they gain the Spellcasting class feature (eg 1st level for "pure" caster classes, 2nd level for rangers/paladins, and 3rd level for arcane tricksters or eldritch knights).
However, if you are mucking with the spell level calculations, could I ask that you please add an option to round up for caster levels when multi-classing? Paladins/Rangers increase in caster level on odd levels (not even) so level 3 is the equivalent of level 2 in a "pure" class (not level 4). Even more striking for rogue/fighter who increase at 3rd and the level after every 3 (eg 3, 4, 7, 10, etc) and not 3, 6, 9, etc. Yes, it is unofficial but it matches the existing spellcasting tables and nobody I've talked to has any idea why they did this as it makes no sense (other than that WotC seems to hate multi-classing) - there's absolutely no reason that if you are a Paladin 3 and then multi-class Cleric 1 that your spellcasting ability should go down (eg it stays exactly the same officially even though you gained caster class levels).