The conference started tomorrow
Solution 1:
There are contexts where a combination of past tense with a future time-reference would be idiomatic and grammatical, as choster remarks in the comment. Consider the following imaginary conversation.
Bob: I'm looking forward to the conference next week.
Mike: It's not next week! It's tomorrow.
Bob: Really? When I checked the brochure it started next week.
This would be an elliptical form of so-called 'reported speech'.
It's possible you heard something analogous.