There are a few reasons you may not see a price change from Aura reflected on Amazon.com right away.
The old price is cached in your browser. To eliminate this variable, open the listing in an incognito or private window, or perform a hard refresh on the page.
Amazon is still processing the price change. As the volume of overall price changes increase, Amazon processes massive amounts of feed-based price change (and other) data. Amazon has noted delays for price update feeds on their blog, here, and in a developer community post, here.
Latency or delays with Amazon updating Aura (via their API) and Amazon.com at different intervals. This may lead to a price being updated on one, but not the other, until it "catches up."
External price movements. This refers to any price change made outside of Aura while repricing is enabled. Manual adjustments in Seller Central, or a different third party tool submitting price changes can lead to "clashing," and Aura's price changes being overridden. This may also lead to Aura's Pricing Activity logs showing mismatching price logging, with external price updates not able to be logged by Aura.
Regional Buy Boxes. This has more to do with Buy Box status, which can change based on where the Amazon.com page is being viewed from. Prime shoppers are especially prone to this, with Amazon prioritizing closer physical proximity (for fastest shipping times) over pricing in many cases, depending where an offers' inventory is physically located.