If your client connects to clearnet relays, and all connections are routed over TOR, you'll hit exit nodes. The only way you can only use TOR would be to use a client that lets you disable clearnet urls and ONLY connect to .onion domains.
Well I was not using nostr .. Anyway it is the same , also if you use tor client if you interact with another mint that it is on clearnrt and don't understand onionaddress , you will have problems ... I don't understood why onion and tor wasn't assumed as base .. LN was assumed to work with tor since the beginning .. So people could choose .. Here it seems that very few wallets and mints work on tor