Interference prediction that accounts for extreme and rare events remains a key challenge for ultra-densely deployed sub-networks (SNs) requiring hyper-reliable low-latency communication (HRLLC), particularly under dynamic mobility, rapidly varying channel statistics, and sporadic traffic. This paper proposes a novel calibrated interference tail prediction framework, a hybrid statistical and machine learning (ML) approach that integrates an inverted quantile patch transformer (iQPTransformer) within extreme value theory (EVT). It captures interference dynamics and tail behavior while quantifying uncertainty to provide statistical coverage guarantees. Its effectiveness is demonstrated by leveraging the estimated interference tail distribution to design predictive, risk-aware resource allocation. In resource-constrained SN scenarios, we introduce the split-iQPTransformer, enabling collaborative training by distributing neural network components between sensor-actuator (SA) pairs and the SN controller, while maintaining minimal performance disparity compared to the centralized iQPTransformer. The framework effectively handles deep fading, random traffic, and time-division duplexing (TDD) misalignments and is resilient to rare and extreme interference events. Extensive evaluations are performed under two mobility models and two realistic SN traffic patterns, using a spatially consistent 3GPP channel model across all scenarios. Experimental results show consistent achievement of block error rate (BLER) targets beyond the 95th percentile in the hyper-reliable regime, significantly outperforming baseline approaches.