He mentioned the palaces would be used for storing grain and then redistributing it among the people, but to me this is pretty much how every other society pre money functioned. I believe it's called a palace economy and I don't think it could be considered communism.
This professor is a PhD in Egyptian history (art history I think?) so he said that in Egyptian trade texts they refer to "the Minoans" as opposed to "George of the Minoans" like they did with other societies. So this to him was proof of a communal society. For example, he says a trader from Rome would be listed as "Julius of Rome traded 5 apples" whereas the Minoans are just "The Minoans traded 4 horses".
I think your professor needs to brush up on their understanding of what words mean. Either that or they used the term "primitive communism" incorrectly, or you've misunderstood them.
I'll state my biases up front, I think capitalism is bad, and workers should control their own workplaces by democratising the role of management. I would love it if a cool society like Minoan Crete used Marxist principles to thrive. However, that simply isn't the case.
Communism as defined by Marx is a Classless Stateless society, in which the workers control the means of production. 20th century attempts at Socialism failed to meet this definition, and followed a Leninist approach which involves using authoritarianism to create "stability" and operate a centrally planned economy, rather than one organised by the workers.
Now, the Minoans weren't classless, if we are to examine their frescoes, paintings and settlement structures it is very apparent that there was a wealthy Elite class depicted as pale women (possibly matriarchal? archaeologists debate this in the pub frequently), and a working class always depicted as darker men. So the Minoans certainly failed to meet the Marxist definition of classless and stateless, and there is no archaeological evidence to suggest a centrally planned economy. Surplus storage and redistribution does not a planned economy make.
There is also no evidence that workers controlled the means of production on Minoan era Crete.
Generally speaking it is -at best- imprecise, and at worse laughably wrong to compare Industrialised economic theory to societies thousands of years ago. It's an example of Presentism, a fallacy many people are guilty of, but a professor should really know better. Having a central store of surplus resources for redistribution during lean times, and for funding public works isn't communism, even though anarcho-communist theory describes how a commune would keep a shared store for emergencies, in the same way that using currency doesn't suddenly make a system capitalist, just because capitalists use currency.
There is a reason the term "Palace economy" exists, and it isn't just pedantry. It is precision, and it is distinctive from other economic systems.
Professors generally love it when a student is willing to argue with them using evidence and logically robust reasoning, so it might be worth bringing this up with them. They might have been trying to bait the class into calling them out on it.