Hmm - I suppose this have to do with the nature of the data. When I try with random data and do a manual calculation (shifting numbers and calculating the integral of the product for each value) it seems to give me the same as JMP does. The lag is -4, which peaks as it should. See the picture.
The thing is that the time series should be filtered for any autocorrelation, something I've read is called whitening. Not mentioned and not possible in JMP in an automatic way as I see it. Anyway - JMP seems to catch my lag of -4 when the data is random.