Despite continued development of effective HIV treatment, expanded access to care and advances in prevention modalities, HIV‐related stigma persists. We examine how, in the context of a universal HIV‐testing and treatment trial in South Africa and Zambia, increased availability of HIV services influenced conceptualisations of HIV. Using qualitative data, we explore people’s stigma‐related experiences of living in ‘intervention’ and ‘control’ study communities. We conducted exploratory data analysis from a qualitative cohort of 150 households in 13 study communities, collected between 2016 and 2018. We found that increased availability of HIV‐testing services influenced conceptualisations of HIV as normative (non‐exceptional) and the visibility of people living with HIV (PLHIV) in household and community spaces impacted opportunities for stigma. There was a shift in community narratives towards individual responsibility to take up (assumingly) widely available service – for PLHIV to take care of their own health and to prevent onward transmission. Based on empirical data, we show that, despite a growing acceptance of HIV‐related testing services, anticipated stigma persists through the mechanism of shifting responsibilisation. To mitigate the responsibilisation of PLHIV, heath implementers need to adapt anti‐stigma messaging and especially focus on anticipated stigma.