Yeah, the username you claim essentially points to the same long address that you already have associated with your npub.

For example, @ek’s address is npub16x07c4qz05yhqe2gy2q2u9ax359d2lc0tsh6wn3y70dmk8nv2j2s96s89d@npub.cash

If he logs in with an extension and purchases ek@npub.cash, he can now use that address instead of the long one.

Going back to cashu.me: if you use your nsec, your corresponding long address will be shown in the Lightning address section. Any sats you receive to either that address or the short one will now appear in your wallet.