As large language models (LLMs) grow in scale and capability, understanding their internal mechanisms becomes increasingly critical. Sparse autoencoders (SAEs) have emerged as a key tool in mechanistic interpretability, enabling the extraction of human-interpretable features from LLMs. However, existing SAE training methods are primarily designed for base models, resulting in reduced reconstruction quality and interpretability when applied to instruct models. To bridge this gap, we propose $\underline{\textbf{F}}$inetuning-$\underline{\textbf{a}}$ligned $\underline{\textbf{S}}$equential $\underline{\textbf{T}}$raining ($\textit{FAST}$), a novel training method specifically tailored for instruct models. $\textit{FAST}$ aligns the training process with the data distribution and activation patterns characteristic of instruct models, resulting in substantial improvements in both reconstruction and feature interpretability. On Qwen2.5-7B-Instruct, $\textit{FAST}$ achieves a mean squared error of 0.6468 in token reconstruction, significantly outperforming baseline methods with errors of 5.1985 and 1.5096. In feature interpretability, $\textit{FAST}$ yields a higher proportion of high-quality features, for Llama3.2-3B-Instruct, $21.1\%$ scored in the top range, compared to $7.0\%$ and $10.2\%$ for $\textit{BT(P)}$ and $\textit{BT(F)}$. Surprisingly, we discover that intervening on the activations of special tokens via the SAEs leads to improvements in output quality, suggesting new opportunities for fine-grained control of model behavior. Code, data, and 240 trained SAEs are available at https://github.com/Geaming2002/FAST.