The methods in the 3rd paragraph of your link state:
The data layers were generated through interpolation of average
monthly climate data from weather stations on a 30 arc-second
resolution grid (often referred to as "1 km2" resolution). Variables
included are monthly total precipitation, and monthly mean, minimum
and maximum temperature, and 19 derived bioclimatic variables.
For stations for which we had records for multiple years, we
calculated averages for the 1960-90 period. We only used records for
which there were at least 10 years of data. In some cases we extended
the time period to the 1950-2000 period to include records from areas
for which we had few recent records available (e.g., DR Congo) or
predominantly recent records (e.g., Amazonia).
So your 2nd option is closest. They averaged records for each month for each climate variable for the period 1960-1990 (with some exceptions), then spatially interpolated the averages and called that "current".