Actually, since the Particle devices run 32bit architecture micro controllers, unsigned long and unsigned int are both 32bit.
Even with distinct uint16_t you would not save any bytes as distinct variables (i.e. not part of an array or packed struct) will be placed on 32bit boundaries.
Also with unsigned arithmetic it's best to avoid mix'n'match and rely on the the compilers implicit type conversions. Since millis() returns a uint32_t it is good practice to also have the other two values of that type.
There is a thread by @rickkas7 that gives some background