It's correct in my opinion. Considering talked to/with and spoke to/with , I think that "talked" has more of a sense of conversation than "spoke" does. That is, it suggests a meeting of the minds.
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"Talked" is used when one has a conversation. talked imply that more words was used back and forth resulting in a conversation. I.e " Tim and i talked, he feels bad and will not do it again"
"spoke" is when it's one sided and you're telling someone something/info. I.e "I spoke with Tim, he won't do that again"
But that being said, you have to take into consideration regional diale