This one is correct. It is subjunctive mood: He insists that she come. This page has a lot of information about the subjunctive and its uses in English.
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I know this is an old post, but note the following:
1) His financial advisor insists that he cheat on his income tax.
2) His financial advisor insists that he cheats on his income tax.
1) is a strong plea to take future action.
2) is a claim that an action regularly occurs.
The same applies to the OP's target sentence.
CJ