I'm unable to parse out what your point is in this post. Perhaps you could reiterate.
If I'm paraphrasing correctly, your point seems to have been that because fire shield requires a creature to hit and because spiritual weapon doesn't specify whether it is the caster, the spectral weapon, or some other agent that hits, but only specifies what happens "On a hit," then it is open to interpretation whether the caster hits when s/he makes a successful attack and therefore whether s/he provokes damage from the shield. Correct me if that's not accurate.
If it's correct, then my response would be that your point fails to comprehend the natural language style in which the rules are written. Variations in phrasing are used interchangeably throughout the text. Most often in the text, it's the attack itself that's said to hit, but sometimes the text mentions the attacker, the weapon, or, in some cases, the spell effect as hitting on a successful attack. And here's the thing: because this is natural language, these variations in phrasing aren't meant to carry any specialized jargonistic meaning. They all describe the same event: a successful attack. On a hit, the attack hits, the attacker hits, and the weapon or spell effect hits. One never happens without the others, so when spiritual weapon says "you can make a melee spell attack", it can be understood that should the attack hit, then you the caster can also be said to have hit. Likewise, when fire shield says "whenever a creature within 5 feet of you hits you with a melee attack", it can be understood that the creature that hit you is the same creature that made the attack.