SpamSieve makes a prediction for every incoming message about whether it is good or spam. It then presumes that its prediction was correct. If it makes a mistake, you need to correct it (always, not just during the initial training). If it was correct, you don’t need to do anything further (because of the presumption).
The initial training is not an extended period of time. It is simply when you train SpamSieve with a bunch of good messages and spam ones (that are not mistakes) in the recommended number and ratio.