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Hello, I'm Dr. Deb and will do my best to help you today.
I'm sorry for this concern for Max but exposure to low levels of this product should be safe.
Spider sprays such as this one contain very low concentrations of pyrethroids which is often less than would be contained in cat flea sprays.
Cats are quite sensitive to concentrated pyrethroids but levels less than 1% are not expected to be toxic to cats. I believe that this product doesn't contain but about 0.1%
Often the biggest concern with a spray of this sort is exposure to the hydrocarbons ( the "inert" or "other" ingredients), which can cause respiratory irritation if inhaled or gastrointestinal upset (nausea, vomiting) if ingested.
However, since Max only ingested a very small amount of this spray off of the spider, I'd not expect any serious systemic effects.
I hope this helps to reassure you about him. Deb