Individualized Alzheimer's disease (AD) progression prediction requires models that use irregular visits, account for censoring, avoid diagnostic leakage, and provide calibrated horizon risks. We propose PROgression-aware MultI-horizon Survival Estimation for Alzheimer's Disease (PROMISE-AD), a leakage-safe survival framework for predicting conversion from cognitively normal (CN) to mild cognitive impairment (MCI) and from MCI to AD dementia using ADNI/TADPOLE tabular histories. PROMISE-AD converts pre-index visits into tokens with standardized measurements, missingness masks, longitudinal changes, time-normalized slopes, visit timing, and non-diagnostic categorical attributes. A temporal Transformer fuses global, attention-pooled, and latest-visit representations to estimate a progression score and latent discrete-time mixture hazards. Training combines survival likelihood, horizon-specific focal risk loss, progression ranking, hazard smoothness, and mixture-balance regularization, followed by validation-set isotonic calibration for 1-, 2-, 3-, and 5-year risks. In held-out testing across three seeds, PROMISE-AD achieved an integrated Brier score (IBS) of 0.085 $\pm$ 0.012, C-index of 0.808 $\pm$ 0.015, and mean time-dependent AUC of 0.840 $\pm$ 0.081 for CN-to-MCI conversion, yielding the lowest IBS among compared methods. For MCI-to-AD conversion, PROMISE-AD achieved the highest C-index (0.894 $\pm$ 0.018) and near-ceiling 5-year discrimination (AUROC 0.997 $\pm$ 0.003; AUPRC 0.999 $\pm$ 0.001), although some baselines had lower IBS. Ablations and interpretability supported longitudinal change features, fused temporal representations, mixture hazards, cognitive and functional measures, APOE4 status, and recent conversion-proximal visits. These findings suggest that progression-aware survival modeling can provide interpretable multi-horizon AD conversion risk estimates.