Learn English – Student’s Book vs. Student Book

When you have a plural word ending with 's', we put apostrophe 'after' the 's'.

Chemistry students' group

A group that consists of many chemistry students. Here, students are 'plural' and you are talking about those plural students' group.

Chemistry student's group

Here, you are talking about a chemistry student (one). The group belongs to him/her.

So, to conclude, apostrophe after 's' talks about more than one student (students) and before 's' talks about a single student's group.

To answer your question simply: an attributive noun is still a noun, it does not become an adjective.

As several commenters have noted, student is being used as an attributive noun, and jailed is being used as an attributive adjective. This doesn't change their classification. Let's take them one at a time.

First, we have "Student Jacob..." with student as an attributive noun. Student is still a description of a (type of) person, even though it is adding itself as an attribute to the proper noun of Jacob. Take it alone, without the proper noun, and we still have a proper sentence: "A student was in Italy."

Next, we have "Jailed Samantha..." with jailed as an attributive adjective. The phrase of Jailed Samantha may be part of a noun phrase, but the word jailed is still an adjective.

As brought up by the commenters, there is another related type of adjective called a Nominalized Adjective which can be used in place of a noun. Take the following sentence:

Jailed protesters began a hunger strike, insisting on joining the freed.

Both jailed and freed are adjectives describing protesters. The first one, jailed, is an attributive adjective and is part of the noun phrase Jailed protesters. Freed is a nominalized adjective which also describes the protesters, but is being used in place of a noun.

Most importantly, however, if the words protesters and the were removed from the example sentence, it would no longer make sense. Attributive adjectives and nominalized adjectives still have to define or qualify nouns, even if the definition or qualification is implied.