Hi,
You can check the implementation of the turn-on delay block by right-clicking the component and selecting "subsystem->look under mask". Further, if you right-click the component and select "subsystem->break library link" you can also change the underlying implementation.
If I understand you correctly you would like to do something like in the attached model? The "monoflop" block from the library might help you building up what you want to achieve.
Best regards,
NF