Jerry,
The others here are getting a bit ahead of me.
My experience tells me that just about everytime there is a difference in timing, the person who is moving first, is ahead of the music.
It is far easier to follow the music, than it is to dance slightly ahead of it.
If you are behind the music, you can easily catch up to the beat. However, if you are slightly ahead of the music, you have nothing to guide you. (I often see these dancers try to catch up to the next measure.)
The ladies at the Senior Center might be a little hard of hearing, or they might just be nervous. (As with a small child, excitement often causes people to move faster than they should.)
I would suggest that you try rocking side to side to the music before you start your figures. (Wispering the count might help too.) Try to get them moving with the music, before you try to lead anything more difficult.
(In answer to your question, my guess is that the ladies are moving early.)