Educational, political, or moral/religious content is increasingly present on TikTok, so contemporary social dynamics legitimize the process of digital mediation regarding these institutional values. Based on 286 open-ended survey answers and subsequent interviews with 45 Romanian TikTok users, this article applies social constructivism to explore the intersubjective side of algorithmic experiences. The significance of such a framework lies in its ability to elucidate the manner in which users actively construct their social environments, which may initially appear as isolated individual experiences but ultimately unveil shared algorithmic interpretations. Thus, the participants highlight three recurrent institutional themes in relation to TikTok’s algorithm: (1) algorithm as political profiling, (2) algorithm as moral plethora, and (3) algorithm as educational benchmark. Findings show that users’ stories related to algorithms are widely conceived within institutional frameworks. These narratives play a role in shaping what Berger and Luckmann call “intersubjective sedimentation” within the intricate interconnection between institutional and algorithmic realities. The ways in which TikTok users legitimize the presence of these institutional actors on their For You page should be seen as a form of agency negotiation between users and machines. The legitimating role of stories about algorithms also highlights the institutional necessity of intergenerational socialization, which is why the contents made by such institutional actors are more and more actively mediated through TikTok.