The mistake is believing this refers to all adverbs, and also believing that one rule can cover all cases. Here is a short introduction, you can see that your rule is about adverbs of frequency, while what your examples contain are adverbs of manner. However, there is a lot more to it, the rules from the link are guidelines for beginner learners, and do not mean that this is the only way to position an adverb in the sentence.

The UGC and universities must work to ensure that the quality of education in the social sciences and humanities is raised.

Paradoxically, rules are for those who have trouble remembering them. So let's take a rhetorical approach instead.

We don't want our adverbs to disrupt the core idea of our sentence, which we can make clear by setting it out as Subject, Verb, Object(ive).

Subject: The UGC and universities
Verb: must work
Object(ive): to ensure that the quality of education in social sciences and humanities is raised.

Imaginatively describes how they must work, so it will precede, interrupt, or follow the verb phrase "must work".

imaginatively must work ... must imaginatively work ... must work imaginatively

In front of "must work" it is premature: we need to wait for the verb to understand it. Between "must" and "work" it weakens the punch of the imperative and is somewhat jarring, for "must imaginatively" yokes the idea of obligation and creativity, unusual companions. Following "work", it becomes an exhortation. That is the desired rhetorical effect, and it is exactly where you have put it.

Appreciably describes the degree to which the quality of education must be raised, so again it will precede, interrupt, or follow the verb phrase "is raised".

appreciably is raised ... is appreciably raised ... is raised appreciably

In front of "is raised" it is premature: we need to wait for the verb to understand it. Between "is" and "raised" it remains premature: we must wait for "raised" to understand what "appreciably" means; moreover, it is slightly jarring insamsuch as "is appreciably" suggests that something can exist and yet be unappreciable. Following "raised", it becomes an exhortation, telling us how much raising is needed. That is the desired effect, and it is where you have put it.

Trust your rhetorical instincts.