Im getting a little nervous( a little long sorry)?

My Husband and I just had twin girls in December.We have 2 older girls too.My husband got a vasectomy in March.He had the procedure done and then was scheduled a date to come back and bring in a sample to the office to see if the procedure was a success.They told him generally it takes about 11 times of ejaculation before its all cleared out of him and no new sperm can be produced and to use protection until he is cleared which we did.Well he took his sample in and they called and said that we no longer needed to use back up that the procedure was a success.I had a period last month and still have not had one this month.I took a pregnancy test like 4 days ago and it was negative.Im just worried because he left his sample in the cup and then drove the 20 miles to the lab to drop it off.It was in a steril cup the doctors office gave him.But doesn't sperm die when air hits it?After he left the sample in the cup it obviously did take a few second to get the lid on.Im worred the surgery didn't take and that the sperm just died.Has anyone ever heared of this happening?We obviously were not planning on any more children.