Context. Nearby young associations offer one of the best opportunities for a detailed study of the properties of young stellar and substellar objects thanks to their proximity (<200 pc) and age (∼5-150 Myr). Previous works have identified spectroscopic (<5 au) binaries, close (5-1000 au) visual binaries, and wide or extremely wide (1000-100 000 au) binaries in the young associations. In most of the previous analyses, single-lined spectroscopic binaries (SB1) were identified based on radial velocities variations. However, this apparent variation may also be caused by mechanisms unrelated to multiplicity. Aims: We seek to update the spectroscopy binary fraction of the Search for Associations Containing Young stars (SACY) sample, taking into consideration all possible biases in our identification of binary candidates, such as activity and rotation. Methods: Using high-resolution spectroscopic observations, we produced ∼1300 cross-correlation functions (CCFs) to disentangle the previously mentioned sources of contamination. The radial velocity values we obtained were cross-matched with the literature and then used to revise and update the spectroscopic binary (SB) fraction in each object of the SACY association. In order to better describe the CCF profile, we calculated a set of high-order cross-correlation features to determine the origin of the variations in radial velocities. Results: We identified 68 SB candidates from our sample of 410 objects. Our results hint that at the possibility that the youngest associations have a higher SB fraction. Specifically, we found sensitivity-corrected SB fractions of 22-11+15% for ɛ Cha, 31-14+16% for TW Hya and 32-8+9% for β Pictoris, in contrast to the five oldest associations we have sampled (∼35-125 Myr) which are ∼10% or lower. This result seems independent of the methodology used to asses membership to the associations. Conclusions: The new CCF analysis, radial velocity estimates, and SB candidates are particularly relevant for membership revision of targets in young stellar associations. These targets would be ideal candidates for follow-up campaigns using high-resolution techniques to confirm binarity, resolve orbits, and, ideally, calculate dynamical masses. Additionally, if the results on the SB fraction in the youngest associations were confirmed, it could hint at a non-universal multiplicity among SACY associations.