There can of course be lots of reasons for crying, all coexisting, and because a child can firmly believe he or she is completely in the right there is no machiavelian scheming, or cunning, involved. But when punished in school, crying for a long stretch afterwards as described by the OP would count in my books as an effort to convince a parent that an injustice had been done, perhaps along with all the other reasons for crying. A parent shouldn't conclude from the crying that a teacher had been unfair or mean or cold towards the child. They shouldn't conclude that their child was trying it on purposefully either, but they should be aware that the child has an egocentric pov here (completely natural and appropriate) and try to show her (as has been done) how others see what has happened.
Fwiw, the discipline method described was never used in my DCs' school until they would have been a year older than Reception or P1 age. Even then there was an intermediate stage between green and red and children had a chance to redeem themselves in the course of the day because quite a lot of infractions had to be accumulated before anyone was moved from yellow to red, and you could move back up too. When they were 4-5 the door was kept shut, and other methods of maintaining order were used.
I don't think that particular method is appropriate for most 4-5 yos. It is too much of a blow to the (healthy and normal) ego of 4-5 yos to see their image or name physically moved to a bad category. Children need to believe the best of themselves at this age and this is done by encouragement of good behaviour along with appropriate verbal reprimands. Conversely, self-identification as occupants of a bad zone can become a self fulfilling prophecy.
They did not use Golden Time in my DCs' school either.
I am not sure loss of golden time at a future date is appropriate either, for 4 yos. A more immediate consequence is better. But I have a lot of reservations about Golden Time anyway.
Being left out of it is a way of shaming a child, which is never good. It also sends a message to the child that staying part of the herd is a good thing. Then when bullying or social exclusion becomes a problem later in school life children are asked not to participate, despite the fact that certain children left out of Golden Time have been visibly not taking part in the pleasant activities and this visible non participation is part of how the lesson Golden Time teaches is intended to work. A reprimand otoh does not physically separate anyone from the group and it should not shame if handled right. (It should correct and teach).
Plus Golden time in general sends mixed messages about work. It is like saying to children 'If you eat all your (disgusting) vegetables, you can have some (delicious) ice cream.' The ultimate end of a teacher is to convince children that engaging in their interesting and challenging work is a joyful experience.