Succeeding a/c may be cleared to climb to previous occupied level once the preceding a/c report leaving that level unless....(not important for that case)
So, you can see there were a mistake regardless rate of climb restriction.
I am not familiar with restriction within documents regarding rate of climb/descent in proc environment but there is always some other restriction higher in priority so you aren't able to apply this.
Doc 4444 intends to cover as much as possible situation so many of them aren't applicable within TMA limits.
Like speed instruction. It is not forbidden but it is impossible to make required proc separation within 25/30 Nm as usually TMA extends(my own TMA and other similar in my neighborhood )
Hope that it helps....
I could explain better but I had hard day today. Brandy season starts. First 50 liters..
Cheers