Digital twins of intensive care patients should update forecasts from new data and predict treatment responses, but few studies test whether routine records support either. We propose ICare-DT, a Transformer-based twin that updates a latent patient state hourly from new measurements without retraining. We trained it on 140,473 eICU-CRD stays to forecast vital signs crossing their training-set means. On test data, later forecasts beat the twin's own hour-6 forecasts of the same windows in all 12 settings (+0.073 to +0.153 AUROC). On validation data, controls that withheld or swapped the new hours traced the gain to the patient's own measurements. Without refitting, the model kept its gain on a second database (8 of 9 settings, +0.025 to +0.114 AUROC) in a prespecified evaluation of the previously analyzed MIMIC-IV test split. Refitted within MIMIC-IV, a twin state fine-tuned on clinical endpoints gave gradient boosting a significant gain for acute kidney injury (+0.0035 AUROC; hypotension +0.0010, not significant). To test response prediction, we built a benchmark that replaces the treatments in real records with simulated doses and injects responses of known size, visible only at measurement times. Ridge models supervised with injected effects recovered them from real records only through frequently measured variables (heart rate) read at their measurement times. We asked standard learners to predict these effects for a dosing regime no patient had received. No standard learner outperformed predicting zero effect at an out-of-support query. When told how the simulated responses were generated, a separate learner recovered the effects from the same records without seeing their true values (R2 0.30 to 0.40 at one effect size). Routine records support forecasts that improve with each patient's new data, and our benchmark is a testbed for models that learn how responses are generated.

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