• insist sb do sth vs. insist sb did sth

Hi!
I read the following in a TOEIC book:

“105. The cook insisted that he ______ the soup to make sure that it was spicy enough.

(A) tasting
(B) to taste
(C) tastes
(D) taste

(Answer: D)”
((Longman Preparation Series for the New TOEIC Test, Advanced Course, 4th Edition, by Lin Lougheed, p. 212))

I agree with the TOEIC book because the correct answer (D) has the omitted ‘should’ in front of it. [SUBJUNCTIVE]

How about ‘(E) tasted’ (past verb)? [INDICATIVE]

I think ‘tasted’ is NOT appropriate for the above sentence, considering the meaning of the whole sentence.

I think as following:

Ex1. [INDICATIVE] Mike insisted that he was right. (RIGHT)
Ex2. [SUBJUNCTIVE] Mike insisted that he (should) be right. (WRONG.)

Ex3. [INDICATIVE] He insisted that she came. (WRONG)
Ex4. [INDICATIVE] He insisted that she would come. (RIGHT)
Ex5. [SUBJUNCTIVE] He insisted that she (should) come. (RIGHT)

Ex6. [INDICATIVE] She insisted that her daughter always came home early. (RIGHT)
Ex7. [SUBJUNCTIVE] She insisted that her daughter (should) always come home early. (RIGHT)

What do you think?
Do you agree with me on ‘(E) tasted’ and Ex1~Ex7?

Thanks in advance.