Figures and their captions play a key role in scientific publications. However, despite their importance, many captions in published papers are poorly crafted, largely due to a lack of attention by paper authors. While prior AI research has explored caption generation, it has mainly focused on reader-centered use cases, where users evaluate generated captions rather than actively integrating them into their writing. This paper addresses this gap by investigating how paper authors incorporate AI-generated captions into their writing process through a user study involving 18 participants. Each participant rewrote captions for two figures from their own recently published work, using captions generated by state-of-the-art AI models as a resource. By analyzing video recordings of the writing process through interaction analysis, we observed that participants often began by copying and refining AI-generated captions. Paper writers favored longer, detail-rich captions that integrated textual and visual elements but found current AI models less effective for complex figures.