Q: Is it legal for a deadbolt lock to have a thumb turn on the inside where the user needs to “push and turn” to open rather than just turn as it is on other deadbolt locks?
A: Section 188.8.131.52.10.2 of the 2012 LSC says doors must be able to be operated with not more than one releasing operation, unless otherwise specified. Section 184.108.40.206.10.6 says two releasing operations are permitted for existing hardware on a door leaf serving an area having an occupant load not exceeding three persons, provided that releasing does not require simultaneous operations.
NFPA does not define what a ‘releasing operation’ actually is, but I think a successful point can be made that a push and turn action could be considered a single action or operation. It all depends on the surveyor or inspector surveying your facility.