In various countries, public libraries play a crucial role in supporting citizens' access to public online services. In Finland, libraries provide both traditional library services and digital support to help customers access their personal bank accounts and health records. However, the impact these new support demands on librarians' expertise and work remains understudied. To address this gap, we interviewed 21 librarians, exploring their experiences in providing digital access services. Qualitative thematic analysis of the transcripts revealed four situational dimensions of digital care work, which encompasses ethical and emotional aspects. We also recommend some best practices for digital access services.