Just to clarify, the OP is asking about the exemption from the Flight Review (under 61.56(d)(1). To add to @Booglebox's answer:
61.1(b) defines:
the "Authorised Instructor" as an FAA Flight Instructor... issued under Part 61, for the Review at 61.56(c)
the Examiner to be "authorised... for an airman certificate or rating under this part", for the exemption.
The key phrase here is "under this part" or "under Part 61". Some sections of Part 61 do not specify "under this part" , and in those cases, other (aeronautical) experience is usually allowable.
If in doubt, you would need an opinion from FAA Legal Counsel, which takes typically a minimum of 6-9 months.
Finally for Instrument experience, 61.57(c) requires the approaches to be both performed and logged. If you cannot document that you were continuously in compliance with para (c) since your last FAA certificate or rating check-ride, then I would suggest that the IPC is required.
As a 61.75 certificate holder, you will never have demonstrated competence to the FAA, unless you have "US Test Passed". If you have a full Part 61 certificate, then the logging is required in a 6/12 month period.
Also note, that while a 'Redbird' type SIM can be used to maintain recency, it cannot be used for the whole IPC, due the need to conduct a Circling Approach.