We study deep-learning surrogates for time-dependent parametric PDEs in an autoregressive rollout setting, where long-horizon accuracy is limited by error accumulation. We propose a parameter-aware encoder-transformer-decoder architecture AE-ViT: a fully convolutional encoder compresses each snapshot to a latent tensor, a vision transformer advances it in time, and a decoder reconstructs the fields. PDE parameters are injected at multiple stages via FiLM-type modulations and a parameter token, and spatial information is provided through coordinate channels. Training uses short-window scheduled sampling to mitigate exposure bias. On a parametric advection-diffusion-reaction benchmark and on 2D Navier-Stokes flow past a cylinder for joint velocity-pressure prediction, we obtain improved rollout accuracy over latent-vector ROM baselines and plain full-field transformer models, with fewer trainable parameters.