The message does not self delete.

What people are seeing is the action of admins to remove the content from your inboxes. A recent Lemmy update provides admins the ability to ban users and remove their content including DMs. The quicker instances are banning the spam accounts very rapidly, some even with automation. The best thing you can do if you receive spam is to report it so your admins can act.

Editing to add- The most recent build 0.19.11 also removes images sent in DMs on the webui. Apps and cached files may still show the images to some users.