The MAX11168 internal reference has a 10 kOhm output impedance, which is why the part features an internal reference buffer. However, there is an integrated 0.1uF capacitor to GND between the internal reference and internal reference buffer. This means the input to the internal buffer charges up to the reference voltage with a single pole RC time constant of (10kOhm*0.1uF) = 1ms. Thus, for a 16-bit converter, you will need to wait for the buffer's input to charge up to within 1/2 LSB of the reference voltage, which can be given by the following equation:
V_REF(1 - V_REF/(2^(N+1))) = V_REF(1 - e^(-t/1ms))
t = -ln(V_REF/(2^(N+1)) in ms = -ln(4.096/2^17) in ms = 10.37 ms
I would wait roughly 11 ms to allow for the capacitor to charge up to within 1/2 LSB of the full reference voltage.