Apollo thinks Eros to be one of his most fascinating devotees. He doesn't know where or how Eros came to know of him, but his fanatical prayers make Apollo feel flattered enough to keep a particular eye on this one.
Mizuki, a fellow gentle soul and bleeding heart, felt sympathetic for the ghost, and eventually agreed to manipulate rain when asked. He feels bad for deceiving the villagers, but he'd feel worse turning away someone with her circumstances.
The more he spends time with her, the more Mizuki finds himself enjoying her company and the more his heart bleeds for her. He often wishes that she wouldn't be so on guard all the time.
Eventually Mizuki realized that either himself or one of his own family members must have coincidentally made it rain just when the ghost made her prayers to that passerby. He hasn't found the opportunity to tell her the truth yet...
Driven by the slightest bit of manic desperation, she pleads with Mizuki to help her create the illusion of having weather manipulating powers by borrowing his own abilities. To her relief, he agreed to help her carry this unfortunate misunderstanding and she is forever grateful for his kindness.
Their continued partnership allowed their bond to deepen to the point where she considers Mizuki to be one of her dearest friends and confidants.