Active exploration in virtual reality (VR) involves users navigating immersive virtual environments, going from one place to another. While navigating, users often engage in secondary tasks that require attentional resources, as in the case of distracted driving. Inspired by research generally studying the effects of task demands on cybersickness (CS), we investigated how the attentional demands specifically associated with secondary tasks performed during exploration affect CS. Downstream of this, we studied how increased attentional demands from secondary tasks affect spatial memory and navigational performance. We discuss the results of a multi-factorial between-subjects study, manipulating a secondary task's demand across two levels and studying its effects on CS in two different sickness-inducing levels of an exploration experience. The secondary task's demand was manipulated by parametrically varying $n$ in an aural $n$-back working memory task and the provocativeness of the experience was manipulated by varying how frequently users experienced a yaw-rotational reorientation effect during the exploration. Results revealed that increases in the secondary task's demand increased sickness levels, also resulting in a higher temporal onset rate, especially when the experience was not already highly sickening. Increased attentional demand from the secondary task also vitiated navigational performance and spatial memory. Overall, increased demands from secondary tasks performed during navigation produce deleterious effects on the VR experience.