Is my traffic routed through your servers?

No.

Tailscale routes traffic over the shortest path possible. In most cases, this is a direct, peer-to-peer connection.

In cases where a direct connection cannot be established, devices will communicate by bouncing traffic off of one or more geographically distributed relay servers, called DERPs. The traffic that bounces through our relay servers is encrypted and no different security-wise than the other dozen hops your Internet packets already make when passing over the network from point A to B.