Phishing attempt immediately after using ING Online

I recently opened a new ING account (Lion Premium). It was all done online and I received the card, the card reader and the card code via normal mail. I logged in the ING web site www.ing.be and finalized the opening of the account as instructed (setting up a password etc). Literally within a few minutes I received an e-mail, supposedly from ING, in Dutch, asking me for all kinds of questions for "security reasons", including my ING ID, the Card ID and password. Luckily I realized that it was a phishing attempt and did not answer. However, the timing just seems really weird to me. I have never ever received an e-mail like that before, and now I get one minutes after I first use the ING online banking. It just seems like too huge a coincidence to me.
Has this happened to something else? I have F-Secure virus protection and firewall on my PC and to the best of my knowledge the PC is not infected with any malware etc. but maybe there is something lurking..