It is challenging for older drivers to transition to manual control after a Take-Over Request (TOR) has been issued by a Level 3 car. This study investigated if the presentation source of the TOR affects driver performance when resuming control. We measured take-over performance, hazard perception, and user acceptance when the TOR was presented on (1) a smartphone displaying a Non-Driving Related Task (NDRT) simultaneously with the In-Vehicle Information System (IVIS), or (2) presented on the IVIS only. Two NDRTs that varied in cognitive demand were tested with older drivers aged 60-69 and 70+. For the lower cognitive demand NDRT, presenting the TOR on the smartphone+IVIS improved takeover performance, hazard perception, and user acceptance, with greater benefits observed in the 70+ group. For the cognitively demanding NDRT, the smartphone+IVIS presentation did not benefit either group of drivers. TOR designers can apply these findings to enhance TORs and assist older drivers in managing control transitions considering the NDRT cognitive demand.