What your regex asks for is:

o followed by n followed by e,
followed by any character (including a newline -- /s switch)
repeated zero or more times
(but as few as possible)
followed by e followed by e
and saved in $1.
[download]

What you'll need to do is use multiple regexes, or multiple captures within your regex:

m/(one).*?(\s\w+ee)\b/s;

That is, match:
o followed by n followed by e
(captured in $1)
any character (including newline -- /s switch)
repeated zero or more times
(as few as possible while still allowing a match)
followed by a whitespace character (\s)
followed by a word character (alphanumeric)
repeated at least one time
followed by e followed by e
(captured in $2)
followed by a word boundary
[download]

It's closer to what you want, though it uses $1 and $2. japhy is right -- your question is a little vague.