When you are experimenting with new things, always run with -w ON:

Scalar value @Array[0] better written as $Array[0] at /tmp/t line 17.
Unquoted string "some" may clash with future reserved word at /tmp/t l
+ine 17.
Scalar value @Array[1] better written as $Array[1] at /tmp/t line 18.
Unquoted string "some" may clash with future reserved word at /tmp/t l
+ine 18.
Unquoted string "more" may clash with future reserved word at /tmp/t l
+ine 18.
main::thing() called too early to check prototype at /tmp/t line 2.
Not enough arguments for values at /tmp/t line 17, near "values]"
Not enough arguments for values at /tmp/t line 18, near "values]"
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But I think your biggest problem is the first line of thing, where you say:

  ($REF_array)=@_;
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That makes a copy of the array. You are no longer assigning to the references to the original arguments, and thus your values are lost once you get out of the subroutine...

I think what you want is more akin to this:

sub thing() {
    ${$_[0]}[0]=([qw(some values)]);
    ${$_[0]}[1]=([qw(some more values)]);
}
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