There must be something wrong with the way you access the array's items. Here's how it's done:
for elem in "${files[@]}"
...
From the bash manpage:
Any element of an array may be referenced using ${name[subscript]}. ... If subscript is @ or *, the word expands to all members of name. These subscripts differ only when the word appears within double quotes. If the word is double-quoted, ${name[*]} expands to a single word with the value of each array member separated by the first character of the IFS special variable, and ${name[@]} expands each element of name to a separate word.
Of course, you should also use double quotes when accessing a single member
cp "${files[0]}" /tmp