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I looked up the word insist in the online oxford learners dictionary
and I read this example and got puzzled

He insists that she come.

she come or SHE COMES ?

which one is right and why ?
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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.
http://www.wordpower.ws/grammar/gramch09.html
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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