In what timeframe was Jataka tales added to Kuddaka Nikaya?
While I have not studied these matters greatly, the Jataka appear of a similar genre to the belated Buddhāpadāna &amp; Apadānas, each found in the Kuddaka Nikaya. 

Based in those suttas where the Buddha is shown to be extremely strict about the purity &amp; accuracy of his teachings (eg, MN 22, MN 38, MN 62, etc), it seems probable after the Buddha passed away, the Brahmanistic elements were entered into Buddhism (such as depicting jhanas as Brahma gods and the gods of the 33) for the primary purpose of spreading the religion, particularly under the zealousness of King Ashoka. 

I think it is important to keep in mind Buddhism became extinct in India due to the Hinduisation of the doctrine; that these ideas about past lives ultimately destroyed Buddhism in the land of its birth. 

SN 22.79 is the only sutta that explains precisely &amp; clearly what is meant by the term 'recollecting pubbe nivasa', which is erroneously translated as 'past lives'. 

SN 22.79 unambiguously states recollecting 'past abodes' means recollecting when in the past the mind mistakenly &amp; ignorantly regarded one or more of the five aggregates to be 'self'. This is perfectly consistent with the essential Buddhist doctrine of 'anatta' ('not-self'). 

Given the Jataka are totally contrary to the instruction taught in SN 22.79 &amp; SN 22.59 and given the Jataka were so destructive to Buddhism, it would appear probable they have no relationship to anything taught by the Lord Buddha.