As far as I can see, ASHRAE doesn't provide a "minimum". If the old website provided a "minimum" based on the ASHRAE data, then it was making a choice as to how often it was likely to actually get colder than that minimum. Hopefully disclosing that choice somewhere, but if not prominently, you may not have been aware of that.
The data excerpted provides an average yearly minimum, along with a standard deviation for that; the minimum temperature in a year will vary from year to year.
If you use the average yearly minimum for your design, then half the years it will be colder than your design temp at some point; half the years it will never quite reach your design temp. [This is assuming the model normal distribution fits the data well, and that the historic data is a good predictor of future results.]
If your project has, say, a 20 year expected life, then you could use the 20 year return period minimum as your design minimum. Then you'd expect that one year over the life of the project, the actual minimum temperature would be less than the design minimum; 19 years it would not.
If that happening one year over a 20 year project is more often than you like, you can use the 50 year return value number. Then you'd have roughly a 60% chance it never happens over a 20 year project lifetime.
So you have to choose your allowable chance of exceedance.
Cheers, Wayne
P.S. If you have one of the old reports, and it specifies the weather station and data set (time period) used, and the new website has the same weather station and option for the same data set, you can compare the old value with the new values and figure out what choice the old website was making.