I’ve been an atheist for the majority of my life, but I was born and raised in a Southern Dwaitin Brahmin family. And growing up, I did get a fair bit of home schooling on the Vedic texts.
The Vedas, which are considered sacrosanct in all surviving sects of theistic Hinduism. There were once atheist sects like the Ajivikas and the Charvakas, but they went out of fashion a long time ago.
The verses in the Vedic texts can be classified in many different ways. For instance, “Bheda Stutis” and “Abheda Stutis” in the Upanishads (which essentially are Dualist and Monist verses). The classification that I’m interested in touching upon here is the distinction between Karma-kanda and the Jnana-kanda (which translate to procedural canon and the theoretical canon). The procedural part mostly deals with the details on rituals and worship (one bit that I vividly remember is the part on the rituals of animal sacrifice, which might come as a bit of a surprise). The theoretical part deals with the questions around the true nature of Brahman (the ultimate god) and Atman (the individual soul). Hindu priests usually specialise in the former (the part involving rituals) rather than the latter. I wouldn’t trust a lone Hindu priest’s opinion on such doctrinal matters. :)
The Vedic doctrine on your question is fairly unambiguous (which is quite rare for anything in the Vedas). The soul (aka the Atman) always takes precedence. The body is considered to be a mere shell in which the soul temporarily resides. Thinking that the body and the soul to be inextricably linked to the body is considered a common fallacy which even has a Sanskrit term for it (Dehatma bhranti). The body (Deha) is considered temporary and dispensable and the soul (Atman), eternal. What happens to the body after death is merely a procedural implementation detail and will not affect your chances at the lottery to attain Moksha. :)
The priest you spoke to probably is confounding the cremation rituals with the idea of sacrifice (aka Bali).