I don't have problems when I receive btc payments through my website.
Although, the fact that you said that it doesn't seem to be doing it any more (copy/pasting is currently transferring the correct address right?) might indicate that this isn't even the reason why you ended up with an incorrect address.
Perhaps you didn't actually copy the address from Electrum correctly and, for whatever reason, already had that address on your clipboard (from a different app/website? )
You would then use another computer that is connected to the internet... and install what is known as a "Watching only" version of your wallet on it. This enables you to see addresses/transactions/balance etc... but you are not able to spend/sign transactions as it doesn't contain any private keys. Refer: https://electrum.readthedocs.io/en/latest/coldstorage.html
The workflow is then... create unsigned transaction on ONLINE computer... transfer unsigned transaction (via USB) to OFFLINE computer... sign the transaction with the private keys (after checking it is all correct!)... then transfer signed transaction back to the ONLINE computer and broadcast it.
It's obviously a lot more work, but is also a lot more secure. However, it wouldn't necessarily prevent your particular scenario unless you take the time to double check and confirm all the transaction details (amounts+addresses etc) BEFORE you sign/broadcast.
What it does do is reduce the chances of any malware on your online computer from being able to access your wallet/private keys/seed etc.
Hardware wallets essentially make this setup redundant, as they achieve the same goal but in an arguably more streamlined, easy to use manner.