Actually there is a 500 type SP exemption via an FFA letter; that's what started this thread.I don't think the 500 type provides for an "SP Exemption". That comes into play with certain of the 560 models. In the 500 and 525 series, I believe you are either typed SP... or not. Upon receiving the type as a single pilot, your new certificate will have CE-500S, or CE-525S listed in your type rating list. Therefore, if your PIC is carrying his certificate, he's qualified as SP.
However, you cannot be typed as a C500S because the plane is Type Certificated (Aircraft Data Sheet) as a TWO-pilot aircraft. If you are performing single pilot operations in a 500 Series aircraft, your Certificate will reflect "CE500". THEN, you must receive an evaluation as to your ability to perform single pilot duties in order to receive an Exemption Letter. This letter MUST be carried as @MidlifeFlyer mentions above.
IF the CE500 pilot chooses to not carry the exemption letter, then two pilots are required for flight per the Aircraft Data Sheet. If he carries it, then only one pilot is required, therefore, only one pilot can log time regardless of whether there is an SIC present or not.
The CE525 is different because it is type certificated as a SINGLE-pilot aircraft.
I can get a CE525 type rating and every one of my CJ flights must include two pilots; both may log time. Once I add the "S" to my Pilot Certificate, things change.
P.S. There is no such Exemption Letter for the CE525. If you want to fly it single pilot, then you have to go get the "S" addition on your Pilot Certificate