"Exclusively sarcastically" means "always sarcastically" or "only sarcastically". Everything this person says is sarcastic. "Sarcastical" isn't a word, the adjective should be "sarcastic". As for when "thanks a million/bunch" is sarcastic: it comes down to voice tone, facial expression and context. If someone looks annoyed when they say it, they're sarcastic. If you just hurt them or made their lives harder and then they say it, it's sarcastic.