Like a number of things, there are a couple pieces needed to arrive at an answer. Run into this in every class and is similar to the discussion over clearance vs. undercut. Chapter 4 references are listed in this order so it hopefully addresses the question in a logical manner. You can really wander into the weeds on this one...
4.8.2.1 and 4.8.2.2 (already provided in this thread) - Sill refers to a part of the building floor structure under an opening and not a threshold, transition strip, etc... Annex A provides a nice drawing to help clarify this and give some context for application of the standard. Doesn't really answer your question, but important to the context of what can/should be under a door. The language was greatly improved with the 2013 edition, but sadly was not adjusted in the two references below which creates a little confusion due to the use of the word "sill".
4.8.5.1 Combustible floor coverings shall be permitted to extend through openings required to be protected by 11⁄2-hour, 1-hour, or 3⁄4-hour rated fire protection fire door assemblies without a sill where they have a minimum critical radiant flux of 0.22 W/cm2 in accordance with NFPA 253, Standard Method of Test for Critical Radiant Flux of Floor Covering Systems Using a Radiant Heat Energy Source.
4.8.2.13* For swinging doors with builders hardware, horizontally sliding doors, and special purpose horizontally sliding accordion or folding doors, raised noncombustible sills or thresholds shall be permitted wherever combustible floor coverings are contemplated or are in use on one or both sides of the door openings.
Here is where my opinion regarding application begins... Typically a transition strip is considered a part of the floor covering 'system'. Therefore, 4.8.5.1 would apply to the transition strip, if placed under the door, since that could be considered a part of the floor covering extending through the opening. One could make the argument (based on other Chapter 4 references) that the transition strip would need to be placed within 2" on either side of the door for NFPA 80 to apply vs. the floor covering reference in the building code. If the transition strip does not/cannot comply with 4.8.5.1, then 4.8.2.13 would allow for an appropriate solution.
Take note that this only applies to 45-90 minute rated openings. 20-minute and 180-minute are different.