This is the relevant CFR to which this regulation applies. I was also told by an FAA check airman that the hours which applies to this regulation had to be accrued under the FAA license. The key phrase in the regs below is '
operations under this part/chapter' which I assume means 'under an FAA license'.
14 CFR 121.436 - Pilot Qualification: Certificates and experience requirements.
§ 121.436 Pilot Qualification: Certificates and experience requirements.
(a) No certificate holder may use nor may any pilot act as pilot in command of an aircraft (or as second in command of an aircraft in a flag or supplemental operation that requires three or more pilots) unless the pilot:
(1) Holds an airline transport pilot certificate not subject to the limitations in § 61.167 of this chapter;
(2) Holds an appropriate aircraft type rating for the aircraft being flown; and
(3) If serving as pilot in command in part 121 operations, has 1,000 hours as second in command in operations under this part, pilot in command in operations under § 91.1053(a)(2)(i) of this chapter, pilot in command in operations under § 135.243(a)(1) of this chapter, or any combination thereof. For those pilots who are employed as pilot in command in part 121 operations on July 31, 2013, compliance with the requirements of this paragraph (a)(3) is not required.
(b) No certificate holder may use nor may any pilot act as second in command unless the pilot holds an airline transport pilot certificate and an appropriate aircraft type rating for the aircraft being flown. A second-in-command type rating obtained under § 61.55 does not satisfy the requirements of this section.
(c) For the purpose of satisfying the flight hour requirement in paragraph (a)(3) of this section, a pilot may credit 500 hours of military flight time obtained as pilot in command of a multiengine turbine-powered, fixed-wing airplane in an operation requiring more than one pilot.
(d) Compliance with the requirements of this section is required by August 1, 2013. However, for those pilots who are employed as second in command in part 121 operations on July 31, 2013, compliance with the type rating requirement in paragraph (b) of this section is not required until January 1, 2016.
https://www.law.cornell.edu/cfr/text/14/121.436