The availability of granular user data allows digital platforms to time interventions with remarkable precision. However, does delivering messages exactly when a user is active truly maximize consumer response? We leverage a novel dataset from a leading push notification provider in China that captures the precise timestamps of screen-on events, inferred from mobile device app usage, and notification delivery. We exploit a quasi-experiment where a user's screen-on timing is effectively random relative to the push request within a short window, creating exogenous variation in the timing gap between screen-on and delivery. Regression discontinuity estimates reveal that, contrary to industry wisdom, immediate screen-on delivery backfires, reducing same-day app logins by approximately 16%. To isolate the effects of different lags, we instrument the realized delay using granular variations in screen-on timing. We find a non-monotonic pattern: users receiving notifications with a modest delay (1-6 minutes) after a screen-on event exhibit peak engagement, surpassing both instant delivery and longer lags. Heterogeneity analysis shows that this penalty for immediate interruption is most pronounced during high-stakes periods, such as weekday mornings. Suggestive evidence from a second live-streaming app and from longer-term outcomes, app uninstalls, is consistent with the main findings. These findings challenge the race for immediacy, suggesting that a modest delay balances intrusiveness against timeliness, making it a variable to optimize rather than an inefficiency to eliminate.