BACKGROUND: Digital public health services (DPHS) succeed when three elements align: dependable operations, clear public-value benefits, and credible institutional trust. How these elements jointly shape user satisfaction across cultures remains unclear. OBJECTIVE: Identify which user-voiced themes relate most to satisfaction, whether legitimacy and civic messages change how complaints affect ratings, and how these relationships vary across cultures. METHODS: We analyzed app-store reviews for two DPHS apps (Indian/UK) using structural topic modeling aligned with Public Value Theory dimensions, public-value outcomes (PVO), operational capacity (OC), and the authorizing environment (AE). Ordered logit models estimated main effects of theme salience on ratings; interaction models tested whether AE cues (institutional legitimacy, prosocial messaging) moderate OC and PVO complaints; a cross-country sensitivity analysis compared India and the UK. RESULTS: OC problems, access, verification, updates, stability, are the most consistent drivers of dissatisfaction. PVO features lift satisfaction only when they deliver end-to-end in real conditions (reliable booking, trustworthy exposure logic, seamless results integration); ambiguous signals or broken data flows quickly erode confidence. Legitimacy and civic cues matter, but not as substitutes for reliability: pairing "trust in government" or solidarity appeals with unresolved core faults typically worsens perceptions; the same cues help when problems are peripheral or visibly being fixed. Cultural differences reshape these effects. In more collectivist, higher power-distance settings, stewardship and shared-purpose framing contribute more to satisfaction once basics work. In more individualist, egalitarian settings, users weigh demonstrable privacy safeguards, transparent evidence, and precise remediation over patriotic messaging. CONCLUSIONS: Make reliability non-negotiable, verify public-value features in live conditions before promotion, and tailor legitimacy strategies to culture. Use civic appeals to amplify, not replace, operational excellence; lead with privacy, transparency, and proof where autonomy expectations are higher. This framework turns Public Value Theory into an actionable playbook for DPHS design, communication, and rollout.