Conversational search systems increasingly provide source citations, yet how citation or source presentation formats influence user engagement remains unclear. We conducted a crowdsourcing user experiment with 394 participants comparing four source presentation designs that varied citation visibility and accessibility: collapsible lists, hover cards, footer lists, and aligned sidebars.High-visibility interfaces generated substantially more hovering on sources, though clicking remained infrequent across all conditions. While interface design showed limited effects on user experience and perception measures, it significantly influenced knowledge, interest, and agreement changes. High-visibility interfaces initially reduced knowledge gain and interest, but these positive effects emerged with increasing source usage. The sidebar condition uniquely increased agreement change. Our findings demonstrate that source presentation alone may not enhance engagement and can even reduce it when insufficient sources are provided.