What is the most real-time method of determining SPI?
There are more up-to-date datasets that are available after registration and acceptance of the respective data usage licences.

E.g. two satellite-derived products


GSMaP https://sharaku.eorc.jaxa.jp/GSMaP/  
TRMM 3B42RT https://mirador.gsfc.nasa.gov/


For a more comprehensive overview, including evaluation against rain gauge data, see Beck et al. 2017.

Beck, H.E., Vergopolan, N., Pan, M., Levizzani, V., van Dijk, A.I., Weedon, G.P., Brocca, L., Pappenberger, F., Huffman, G.J. and Wood, E.F., 2017. Global-scale evaluation of 22 precipitation datasets using gauge observations and hydrological modelling. Hydrology and Earth System Sciences, 21(12), pp.6201-6217.