So you've image and video fields conditioning the display of a Custom HTML field? That won't work reliably in profile edit because there's no input value to scan for since the file input is cleared after the upload is completed. The best way to condition against those types of fields is to use a static condition, which can be done as follows.
Field: Custom > Value
Custom Value: [FIELD_NAME]
Operator: Is Not Empty
This won't take affect until the page reloads. On profile the reason why your condition works is because profile conditions don't look for an HTML input to bind to. Profile conditions are actually just forcing the static condition above under the hood.
Have added a feature ticket to see if built in fallback behavior can be added for file type fields.
forge.joomlapolis.com/issues/8019