Noise-based backdoor attacks on diffusion models typically rely on input-time trigger injection, untargeted activation, and out-of-distribution target generation. Such assumptions reduce both the stealthiness and the practical relevance of these attacks. In this work, we present TEMPO-Diffusion, a targeted backdoor framework that localizes the malicious distribution shift to a temporal, in-distribution exposure. TEMPO-Diffusion supports: (i) targeted attacks on and to specific classes, (ii) multiple sub-image backdoors that reconstruct specific features within multiple, different output images and at multiple locations, and (iii) in-painting with time-conditioned triggers. To study relevant, practical security concerns in leveraging backdoored diffusion models for synthetic training data, we also introduce CALISA: a balanced, region-aware traffic-sign dataset emphasizing Canadian and U.S. road signs. Across CIFAR10, GTSRB, and CALISA, our experiments show that TEMPO-Diffusion can reliably poison class-specific synthetic data generation and induce high attack success rates in downstream classifiers trained on that data.