The reason why IRCC requires applicants to submit a police certificate if they have spent 183 or more days in another country during the preceding FOUR (4) years is
this is the period of time prescribed by Section 22(3)(a) in the Citizenship Act (this should link), which provides that a criminal conviction in another country during the "
four-year period immediately before the date of the person's application" prohibits eligibility for a grant of citizenship. So IRCC requires proof of no such conviction for any country in which the applicant has spent a significant period of time, which IRCC has administratively set as 183 or more days in total during that relevant time period.
This has nothing to do with when the applicant came to Canada or with the presence requirement.
This has been discussed in-depth in numerous threads here.
Reminders:
-- if it is unreasonably difficult to obtain the police certificate,
the applicant can explain why RATHER than provide the police certificate; this will almost certainly pass the completeness check; IRCC may address the validity of the explanation later in the process
-- generally a police certificate will suffice if EITHER it has been issued within the six months prior to applying, OR if it has at least been issued AFTER the applicants last time in the other country
Edit-to-add: Or, as
@btbt observed, an applicant who has not been in the other country for the last three plus some years can wait longer to apply, wait long enough that the total number of days in the other country during the relevant four years is less than 180.