There’s no way siècle can be pronounced [sjɛkla], it definitely is not an [a] sound at the end of siècle but a schwa ([ə]). The recording you link to is not very good, machine produced with too much stress on the second syllable, hence your confusion maybe. Listen to the word on shtooka* and I hope you can hear the difference, the difference is striking to those who can speak French.

This being said there’s no need to represent the schwa in the IPA transcript of siècle (and for most words ending with the letters “le”) because pronouncing the sound [l] automatically induces a schwa, there’s no way it can be pronounced otherwise. So most IPA transcripts of siècle are [sjɛkl], although some choose to represent it [sjɛklə], as here for example, in my Robert Collins English-French dictionary it is represented like this: [sjɛkl(ə)].

*_{Recordings on Shtooka are made by real natives and not machine produced. The are made by volunteers and are free to use by all.}