Looking at the dictionary, I read that should has origin as past tense of shall. In the modern English, is should ever used as past tense of shall?
ORIGIN Old English sceolde: past of shall.
should is the preterite form of the modal verb whose present form is shall. As such, should can be (and is still) used in the past tense, in places where shall would be used in the present tense.
Other modal verbs that follow the same pattern are will/would, may/might and can/could.
Giving examples of reported speech doesn't illustrate that modal verbs have tense. The backshift to the Historical past tense forms, of modals, that only sometimes occurs doesn't express a true tense shift. It only tells those in our speaking/writing audience, that by making this replacement, that we are not directly quoting what the original speaker said.
If this was actually a true shift in tense, we wouldn't be able to quote someone directly because that important tense/time shift wouldn't show up and there would be considerable misunderstanding.
Let's look at an example:
Charles: I need some paper.
Brett: What did Charles say?
Jane: He said that he needed some paper.
When Jane used 'needed', the past tense form of 'need', she wasn't saying that the need has disappeared, that the need has been met, that Charles no longer needs paper. Using the past tense FORM is just a signal, not the actual shift that we see when an event is actually finished.
Jane: He said that he needed some paper but he got some from Art, so he doesn't need any now.
Noldorin is at least partially correct. Modals are a special class of verbs which carry various modal meanings into sentences.