Import doesn't use the current collection — it imports everything into your library, and the only option is whether to also add the items to a new collection.

If you want to add all the items to a given existing collection, you can either a) tell it to create a new collection, drag all the items to the existing collection, and delete the import collection or b) sort the library by Date Added descending and drag all the newly added items to the collection. For a small number of items, you can also use Import from Clipboard, which does use the current collection.

And, obviously, when you save from the web, which is the standard way of adding things to Zotero, you can choose what collection to save to.

We could consider making it possible to choose an existing collection for imported items rather than creating a new collection.

@homunculoid: This already changed in Zotero 7, which imports into the current collection if you uncheck that option.