Large Language Models (LLMs) have been widely used to support ideation in the writing process. However, whether generating ideas with the help of LLMs leads to idea fixation or idea expansion is unclear. This study examines how different timings of LLM usage - either at the beginning or after independent ideation - affect people's perceptions and ideation outcomes in a writing task. In a controlled experiment with 60 participants, we found that using LLMs from the beginning reduced the number of original ideas and lowered creative self-efficacy and self-credit, mediated by changes in autonomy and ownership. We discuss the challenges and opportunities associated with using LLMs to assist in idea generation. We propose delaying the use of LLMs to support ideation while considering users' self-efficacy, autonomy, and ownership of the ideation outcomes.