To understand how your privacy is protected you must understand how tracks are followed.
For this example let's say the recipient is an Electrum Bitcoin wallet. Public records will show bitcoins have been transferred from the exchange wallet.
Law enforcement will require the exchange to give all information they have on this transaction: a Monero hash (untraceable) and an IP address: the one we used to call the exchange.
This IP is owned by a proxy rotator to make sure exchanges cannot identify our service. Law enforcement will also need this proxy rotator service to give information on the caller and buyer of their service.
We used Monero to pay for proxy rotators and Tor to access and make calls. Even if they get to this point we are still a ghost. If they terminate our account we will use backups rotators to ensure service availability.
In the worst case scenario they magically find the ip calling and get to our service, by that time your order will already be deleted.
If you still have suspicious thoughts just make sure to delete the order before you use the funds on the recipient wallet.