Anomaly detection aims at distinguishing between in-distribution samples, which belong to the same distribution as the training set, and out-of-distribution samples, which lie outside of it. In textual anomaly detection, recent approaches routinely apply anomaly detection algorithms directly to embeddings extracted from pre-trained embedding models (two-stage approaches). However, the geometric properties of pre-trained embeddings can hinder the effectiveness of detection algorithms, which often rely on distance-based measures. In this work, we first highlight the relevance of similarity-trained models for textual anomaly detection. Beyond being trained to capture semantic similarities, these models also exhibit geometric properties that appear better suited to detection algorithms. We further demonstrate that, besides model choice, a simple post-processing step can significantly improve anomaly detection by adapting embeddings to the assumptions made by classical detection algorithms. The bulk of our experiments is done on a reformulation of the classification tasks from the MTEB benchmark into anomaly detection tasks.