Most browsers create and maintain a "cache" of recently viewed sites, images and other data. Sometimes we can set RAM limits for determining how much disk space that cache can use. As far as I can tell, Safari does
not offer that capability. However, in the
Safari Prefs,
Advanced tab (at least in
Catalina macOS 10.
15 and
Big Sur macOS
11, there is a checkbox for enabling the "Develop" menu in the app. The main thing that might then be useful to you in that menu is the "
Empty Caches" item. It is possible that your browser is simply not "seeing" your new images as new, especially if these images are always the same name.
Adding the "Develop" menu won't require restarting Safari and you can even set a short key(s) for its use! If it does not help you can always UN-check the setting in Safari Prefs. Hope that helps.