I am being a bit pedantic here, but yes, the witnesses must both sign in the presence of the testator. But YES they can sign at different times. And the order is slightly wrong.
First requirement is that the signature of the testator (or the signature of someone else, in the presence of and at the direction of the testator) is made or acknowledged in the presence of the two witnesses present at the same time. Each witness then "attests and signs" the will OR acknowedges his signature in the presence of the testator but not necessarily the other witness.
Here is an example. Fred signs his will in front of Bert and Geoff. Geoff then attests and signs the will in the presence of both. An hour later Geoff and Fred leave the room and Bert signs the Will alone. Fred returns and Bert points to his signature on the Will and says "See Fred, I have signed your will, that is my signature". Will is completely valid.
And funnier things have happened. I recall a case where just after the little old lady died, one of the witnesses phoned the solicitor and said "is everything alright Mr Smith? Cos I signed Mabel's Will and I knew it was her signature, but she wasn't there, her gardener brought it up to the house"!!!!! Will was declared invalid.