do as (one is told/ordered…)
in accordance with
in compliance with
just like
Structure
*Verb[passive] + (が) + まま + (に)
[Verb[passive] + が + ままに is an older form and not very common nowadays]
[A[passive] + まま(に) + B is used to express that B is done in compliance with A, without any opposition or deviation. A is usually a request, order, desire, instruction, etc.]
[The verb in passive form is non-past]
[とおり and ように are more common ways to express this grammar point]
For the example sentence
苦い経験：「説明書に書かれているままにノートパソコンを組立て直したつもりだったけど、ネジが1本残っている。」
Bitter experience: “I thought that I had reassembled the laptop as written in the instructions, but I ended up with one screw left over…”
This one is the only example where ている used, and there’s no special explanation given in the grammar point. Is this stative usage, expressing the instructions were written (and remain in the state of being written)? I suppose you would use ている because the past tense isn’t used?