It depends entirely on whether the assistant is reading the live web or answering from a fixed training cutoff, and most of the major ones now do some of both. When an assistant browses — Copilot and ChatGPT against Bing, Perplexity against its index and the open web, Gemini against Google, Claude through its own retrieval — a change you publish can show up within days of being crawled and indexed, which is why submitting pages and pinging IndexNow matters. When it answers from training data alone, the picture of you is frozen until the next model update, which can be months, and nothing you publish moves it in the meantime. The practical implication is that the fastest lever you control is the live-web path: make your pages crawlable, keep your facts consistent so freshly-crawled content agrees with what the model already half-remembers, and push updates to the indexes that feed browsing. You cannot force a refresh, but you can make sure that when a crawl happens, it finds a clear, current, consistent version of you.
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