Payments are made once the balance of a tip jar exceeds 0.01 BTC, this is to cover the network transaction fee and prevent possible abuse of the service.

This is a known limitation, and it's been built in by design.  The issue is that direct messages on Twitter can only be used when users already follow one another.  So this version allows you to openly publicize people and causes you want to support.

The next version will be released very, very soon and will give you the added private features you're asking about now. So just stay tuned!

I have implemented @PayBitBack, the Bitcoin Tip Jar for Twitter. See http://forum.bitcoin.org/index.php?topic=14707.0 for the announcement.

PayBitBack, The Bitcoin Tip Jar for Twitter
      Makes Sending Money as Easy as a Tweet!

Donate Bitcoins to any Twitter user even without knowing their Bitcoin address.

Amsterdam, The Netherlands, June 10, 2011
See http://www.paybitback.com/ and @PayBitBack

I am looking for the select few from the BTC community who want to be the first to give our
new Bitcoin-for-Twitter service a try. The first users to follow the instructions below will be
able to send and receive Bitcoins for free just by sending short messages to @PayBitBack.

Please take a look at http://www.paybitback.com/ or see the instructions below.
We are working on more compelling features which will soon be announced!

PayBitBack lets you create a tip jar to support your friends, Twitter celebrities, favorite
causes, girlfriends and cleaning ladies.

Actually, you can send Bitcoins to anyone with a Twitter account, even if they don’t have a
Bitcoin address yet. PayBitBack keeps the coins securely for the account holder until they
claim them.

INSTRUCTIONS

Create a tip jar.

Mention @paybitback in a tweet to someone to create their Bitcoin account.
Tweet: @friend you now have a tip jar @paybitback

PayBitBack will reply with a tip jar for them. Retweet it to further promote this cause!

Example reply:
@yourname donate #bitcoin for @friend to 1Dx2DxR3jRR47VBcyDUzEe7a21HRBGm8aR

Now send some Bitcoins to the address provided by PayBitBack.

Claim your tip jar.

If you receive Bitcoins via PayBitBack, @paybitback will notify you via a tweet. For example:
@yourname you have X #bitcoin in your tipjar, tweet me your bitcoin address to claim

Then you can confirm your claim and automatically forward all current and future tips
to the address you specify. This is done by tweeting: @paybitback yourBitcoinAddress

Example: @paybitback 16d7hYxSLQLQJy63iLyukxE2HzzmnP2HAG

PayBitBack will confirm your claim and automatically forward all current and future tips to your Bitcoin wallet.

Example reply:
@yourname thanks. Your #bitcoin tips will be sent to 16d7hYxSLQLQJy63iLyukxE2HzzmnP2HAG


(Edit: Updated sample reply for tip jar creation.)