See if this helps:
We tend to refer to "CFI" in conversation as a CFI with an Airplane Single Engine rating, with CFII, CFIMEI being the only ones where we refer to the rating independently. But that's not really accurate.
There is a CFI certificate. Like pilot certificates, CFI certificates have associated ratings. There is nothing the the FARs or FAA policy that insists that your first CFI checkride has to be, for example, a CFI-ASE (a CFI certificate with an airplane single engine rating). It's up to the applicant what to apply for.
Until fairly recently (about a year ago), FAA policy was to permit a CFI whose only CFI rating was "Instrument Airplane" to teach instruments in any airplane that the pilot had a rating for on his Commercial Pilot Certificate. So, a CFI-IA (only) could teach instruments in a twin if the CFI also had a Commercial Pilot Certificate with an Airplane Multi Engine Land rating. But no more.
"Certificate." "Rating." We sometimes tend to use those terms interchangeably, but they mean very different things.