When you publish a collection, the app builds a public copy for your students, and on that copy it only keeps images from Unsplash (images.unsplash.com). Any other image — including your postim.cc artwork — is dropped, and since your cover isn't an Unsplash link either, the app auto-fills the cover with an Unsplash photo. Your own cards still look right because your private view shows your original URLs; only the published copy is filtered.
The reason it's Unsplash-only is curation: published collections are public and seen by all ages, so we restrict images to a source that's moderated and known to be appropriate. The side effect is that composite art, which Unsplash won't host, currently has no path onto published cards.
The .csv route you mentioned is the way to keep your art, and it works because personal cards aren't filtered: export your collection to CSV (the image URLs are included) and have students import it — your images will show on their cards just as they do on yours.