That's right, it doesn't. Refer to my earlier post expressing disappointment with the design work. SSI joins an ignoble list of game rules that contain lacunae: incomplete as written.
Unless you take in account that it's not casting a spell so the general formula may not apply and the item is producing the effect which also brings in the whole "who's proficiency is it anyway?" Problem even if you use the general spell casting rules.
That's a subclass feature from a different class. Helps the RAI argument but as far as RAW go it doesn't apply.The same formula is used for not casting spells too. Go look at fighter attacks and DC's.
The spell casting rules in the PHB govern your spells which would excludes those rules as well if the spells are deemed to be originating from the SSI which is the base of the "it's not spell casting" ruling which has been verified by sage advice.
So far as I know, there is no general rule for spell effects produced from items. A group might feel the SSI to be similar to a ring of spell storing, which users the original caster's stats. One puzzle will be why SSI references only the artificer's ability modifier? Elsewhere, where such limited language is found, it means what it says: use only the ability modifier, not proficiency. Still, most (perhaps all?) items - from scrolls to rings to wands - that store spells that are later cast or produced from them do use values that match an original caster's stats. If there is an intended general rule, then I believe that provides relevant context.
The general rule is it is treated as a spell unless it says otherwise in the description.
