Incorrect: It is essential that you are on time.
Correct: It is essential that you be on time.

Incorrect: He suggested that we should meet at the train.
Correct: He suggested that we meet ate the train.

Please can you tell me what is the logic behind using "be" instead of "are" in the first sentence with "essential" and using "meet" instead of "should meet" in the second sentence with "suggested". Can you name this error or specify any key words for this error. I've taken these sentences from Barrons Gmat Guide and thae call it "Errors in verbs followed by verb words" but I can't find any sources for this topic on the internet.
Thank You.

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