It's not about proving residency. It applies to all existing Turkish bank account holders, not just expats and is linked to the EU's Anti-Money Laundering policies. In the the past Turkish banks have accepted almost any address without proof. Now they are having to bring their systems up to date.
It was originally to be the 1st January but it was put back to the 1st June after protests to government from the banks.
Although, individual banks are are putting a different June deadline on it, the rule is that you should provide proof of address in either Turkey or your home country to your Turkish bank in the form of a copy of a utility bill in the name in which the bank account is held, by the 1st June 2009 or your account will be frozen until you supply the required information.
However, if you pay any of your Turkish utility bills by direct debit, you shouldn't have any problem as you would have had to produce the necessary document when setting up the DD at the branch.