The double quote pairing is in fact correct

# /^set\szone\s("([^"]*)"|id\s\d+\s"([^"]*)")/
#              ^       ^            ^     ^
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Yes, it is actually the first format which has the right parenthesis in the wrong place. But, as you say, that wasn’t the OP’s problem either.

No. The OP's parenthesis matching really is correct - all of it. The parenthesis pairing is:

#              v                            v
# /^set\szone\s("([^"]*)"|id\s\d+\s"([^"]*)")/
#                ^     ^            ^     ^
[download]

The OP's issue is that the parenthesis marked with 'v' are the $1 capture group. The two sets of parenthesis marked with ^ are what the OP hoped were $1, but really they are redundant grouping parenthesis.