AFAIK, there is no real difference between adjectives and verbs in terms of when to use their past-tense or non-past forms with 時. Both forms are valid and useful, but they do not mean the same thing.
I think the trick here is to understand that there's nothing really special (grammatically) about the 時 constructs: 時 is just a noun, which means "(a/the) time(s)". If you put a verb/adjective/clause/etc in front of it, that just modifies the noun 時 to be more specific about which time(s) (i.e. the specific point(s) in time) you are referring to, so you can just think of this general construct as saying "the time(s) when (verb/adjective/etc is/was/will be true)". So:
- 暑いとき -- "the time(s) when (it) is hot" --> "at hot times", etc.
When the modifying clause is in the past tense, that actually says that at the point in time we are talking about, that action/event/condition/etc had already happened, so:
- 暑かったとき -- "the time(s) when (it) had been hot (previously)"
On page 353 of your book, there is actually an example (with する instead of an adjective) which demonstrates this fairly well, I think:
This actually uses 時 twice, and if you'll note, one of them is using non-past tense (食事をする時), but the other is using past tense (した時). Why? Because in the first case, it is saying "at time(s) when we will (are about to) eat" (at the time we're talking about, the action hasn't happened yet, hence present/future tense), and the second one is saying "at time(s) when we have eaten" (at the time we're talking about, the action has already been completed, hence past tense).
As you might be able to guess, talking about "the time after some adjective had previously been true" isn't usually as common a sort of thing to be trying to say (compared to saying "the time after some event happened", etc), which is why the past-tense form with 時 isn't used as often with adjectives as with verbs, I think. However, the intrinsic meaning is still basically the same in both cases. It just depends on whether we're saying the adjective/verb is/was the case at that specific time, or it had been the case previous to that time.