***** NOT A TEACHER *****
Aachu,
(1) The "correct" answer is "It is (high) time that everyone told them to shut down their rumor factories."
(2) Since you are a learner, it is a good idea if you always use the past tense (some
people prefer "past subjunctive")
form after "It is (high) time that ...." ("High" makes it stronger.)
(3) And remember: never use the "s" form after "It is (high) time that ...."
(4) NEVERTHELESS, please do not be astonished if you occasionally see a "It is
time that ...." sentence that uses the present tense (some people prefer "present
subjunctive").
(a) Here is an example from a famous English helpline on the Web:
(i) It is high time we send him a letter. (We have a plan to do something real.)
(ii) It is high time that we sent him a letter. (We are sorry that we have not sent him a letter. We may or may not send him a letter. It's a "wishful thought.")
Source: Grammar Logs # 471.
(b) Here are some examples from a famous grammarian named George O. Curme:
(i) It is high time that he go. [Remember: no "goes."]
(ii) It is high time that he went.
(iii) It is high time that he were going.
(iv) It is high time that he should go.
Professor Curme says that (ii) - (iv) are more "modest." That is, they are NOT so demanding as (i). `As the Grammar Logs said, (ii) - (iv) are "wishful thoughts."
Source: A Grammar of the English Language.
(5) It is only my opinion, then, that this would also be "good" English:
It is high time that everyone tell [remember: no "tells"] them to shut down their rumor factories. [As the Grammar Logs said, this might mean that you and others are making plans to shut them down -- sending in the police, passing legislation, etc.]
"It is high time that everyone told them ...." might be just a "wishful thought," as the
Grammar Logs said.
*****
To sum up:
(a) While you are a learner, make things "easy" by always using the past (subjunctive) after "It is (high) time that ...."
(b) If you see a present (subjunctive) form, remember that the sentence may also be
correct.
P.S. If any teacher disagrees with something in my post, you should believe him/her.