Let’s assume, you’re using Tor to connect to Google. Your traffic will pass through various Tor relays, but in the end, your traffic will transfer from the Tor network and then hit Google’s server. Most of the traffic comes eventually from the Tor network. The system you’re using may initiate the connection, otherwise, it may act as the relay and will move the traffic to the next Tor node.
It is not possible to actually detect which computer has requested the traffic. It means your traffic passes through several randomly picked relays before finally leaving Tor’s network. When you browse through Tor, your internet traffic starts routing via Tor’s network. However, it’s a powerful tool that strongly maintains users’ anonymity.
Tor is not the most secure browser so I wouldn’t say that it’s 100% safe.