Controllable Automatic Text Simplification (CATS) produces user-tailored outputs, yet controllability is often treated as a decoding problem and evaluated with metrics that are not reflective to the measure of control. We observe that controllability in ATS is significantly constrained by data and evaluation. To this end, we introduce a domain-agnostic CATS framework based on instruction fine-tuning with discrete control tokens, steering open-source models to target readability levels and compression rates. Across three model families with different model sizes (Llama, Mistral, Qwen; 1-14B) and four domains (medicine, public administration, news, encyclopedic text), we find that smaller models (1-3B) can be competitive, but reliable controllability strongly depends on whether the training data encodes sufficient variation in the target attribute. Readability control (FKGL, ARI, Dale-Chall) is learned consistently, whereas compression control underperforms due to limited signal variability in the existing corpora. We further show that standard simplification and similarity metrics are insufficient for measuring control, motivating error-based measures for target-output alignment. Finally, our sampling and stratification experiments demonstrate that naive splits can introduce distributional mismatch that undermines both training and evaluation.