A rough summary of the data construction procedure is as follows (for detail, see Deichman et al. 2001). They first collect the spatial data on national and sub-national administrative boundaries and the population estimates at the level of these administrative units. From these two data sources, the population density for each administrative unit is calculated. If a 2.5 arc-minute grid cell falls within one administrative unit, then, the population density of that unit multiplied with the area of the grid cell is used. If a cell falls onto more than one administrative unit, each unit's population density is multiplied by the area of that unit in the cell and summed over. In the calculation of areas, the water bodies and the presence of ice are taken into consideration.
Version 4 is expected to be released during 2016. The spatial resolution will be at the 30x30 arc-second cell level because the input population census data is more spatially disaggregated than for Version 3 (see here). Using the population data from census conducted between 2005 and 2014, the data for years 2000, 2005, 2010, and 2015 is constructed by extrapolation with the population growth rate based on the comparison to the previous round of census. See here for detail on extrapolation.
According to Campante et al. (2015), "the autocorrelation in the measure of population concentration is very high across the ten-year period in question. .... 1990 ... is judged by the SEDC as having the highest data quality."
Used also by Quoc-Anh Do and Filipe R. Campante (2007) "Keeping Dictators Honest: The Role of Population Concentration" to measure an index of population concentration around the capital city.