client.get is asynchronous
This code is working, then you have to manage your code to wait for asynchronous response.
client.get('statuses/user_timeline', function(error, tweets, response){
    if(error) throw error;
    console.log(tweets)
});
If you have some code after client.get, you should do that
before :
var userTweets = client.get(..., function() {});
// do some code
console.log(userTweets);
after : 
client.get(....., function(error, tweets) {
   ...
   otherCode(tweets);
});
function otherCode(userTweets) {
   // do some code
   console.log(userTweets);
}
I suggest you to read this answer : https://stackoverflow.com/a/11233849/5384802 to understand asynchronous code.