Hi Kozo,
Looking at your schematic, no resistor is connected across the positive high voltage rail (10 uF E-cap + pin) and the pin 1 or EN/UV pin of TNY274G. This means that the line undervoltage feature of the device is disabled. If this feature is not use, the flyback should turn-on approximately around 30 VDC. But with or without the line undervoltage functionality, the delay from the input voltage to output voltage regulation is only for few msecs, around 10 - 15 ms (also dependent on the output load) and shouldn't reach 0.5s.
Then Just to give you a brief discussion with regards to RDR-248, as you can see on the schematic of the auxiliary which uses TNY274GN device, R26 and R27 is connected across the positive bulk voltage to the EN/UV pin of the IC, which means it utilizes the Line UV feature of the IC. Using this values the line undervoltage will be around 87 VDC. As you can see on its test data regarding the Brown-In testing, the measured auxiliary supply brown-in threshold is 61.7 VAC, approximately equal to the target line undervoltage. During this time the current that flows to the EN/UV pin exceeds 25uA (based also on calculation having a line sense resistor equivalent to 3.3M-Ohm, the current that will flow to the EN/UV pin will exceed 25uA at approximately 87 VAC). Once exceeded the threshold current of 25 uA, the BP/M pin voltage will rise to 5.85V from 4.9V, that would initiate the switching of the primary MOSFET and eventually the output.
Without the line undervoltage resistor, as in the case of your schematic, the delay from the input voltage to output regulation should also be in the range that were mentioned above. Except that power supply will turn at low voltage input, in example at 30VDC, if line undervoltage is disabled.

Maybe if you could help to capture some waveforms, we could analyze it more further.
You can monitor the following points in your circuit at the same time:
Channel 1: DC Input Voltage (across the 10 uF E-cap).
Channel 2: Pin 1 or EN/UV pin of the TNY274G.
Channel 3: Pin 2 or BP/M pin of the TNY274G.
Channel 4: Output Voltage across C7 (output capacitor).
Then next include the measurement of Drain-to-Source of TNY274G. Remove the oscilloscope probe at EN/UV pin and replaced it with the probe monitoring the Drain to Source of the IC (across Pin4 (Drain) and Pins 5,6,7,8 (Source).

Put a oscilloscope probe from each point, then slowly or gradually increase the DC input voltage or apply the DC input voltage from 0 VDC to 80 VDC.

And just have some following questions:
1. What is the highest calculated load of your 18 V output (18 V that supply the IC regulators)?
2. Can you give the complete part number of the optocoupler and zener diode that you are using?
3. Though already indicated in your schematic that the output voltage or supply of the IC regulators is 18V, what is the actual or measured voltage (the voltage across C9 and C10)?

Another recommendation is if you can also isolate the output voltage across C9 and C10 from its connection to post regulators and the diodes. Isolating, meaning removing the IC regulator IC2 and IC3 and diodes D5 and D6. And just connect the output of C9 and C10 to the E-load. And see if the post regulators have some impact in the operation of your auxiliary or pre-regulator (TNY274G operation).

Hi Kozo,
For your second question regarding the Revision Note G which states that "Update line undervoltage threshold is 2 mA".
Actually this is a typo error, it should be 2uA. It was from 1uA then it was revised to 2uA.
The IC uses this to detect if line undervoltage is unused or disabled, usually if the design requires low voltage input.
Similar to your schematic, no resistor/s across the high voltage positive rail to EN/UV pin, making the line UV feature disabled. So essentially your power supply should powered up even at lower input voltage, that I also mentioned in my first response.