So you bought this account just recently?
No way you could have been a bitcointalk member for 2 years without ever reading this frequently (asked/answered) question.
I have been on the forum a long time, have seen this brought up frequently. I KNOW the standard answer is "extremely unlikely". It doesn't mean I am convinced by this standard answer. "Extremely unlikely" doesn't bring much sense of safety to be honest.
I understand why OP is suddenly worried after 2 years of using bitcoin. Because 2 years is about the time when he accumulates enough bitcoin to be worried about loosing it.
So is it his website real or just fake?
Do we have to worry about is?
It's fake. I have read from somewhere that the site only calculates the address from keys when someone click on the link.