Looking at the code of Exporter.pm, nothing is explicitly exported in both cases. What's happening here?

Exporter has only been exporting the import routine since 5.8.5 (possibly 5.8.4 but I don't have it handy to check). By explicitly exported do you mean something like @EXPORT_OK = qw( import );? It would have been possible for Exporter to do it that way but actually it's done directly in Exporter's import method.

If you want to be backwards compatible you need use inheritance or the other suggestions above.