Since the receiving wallet is saved under the kind-0 metadata it will be shared between web and mobile clients because it is fetched from the relays. Hence, if your connected wallet is linked with your profile you will receive zaps normally somce your profile includes the receiving lightning address. For your concern the experience is a bit different with the web, whenever you log out the wallets the local cache is clearsd out, hence the wallets wont be existed anymore we will see what we can do about that.