[Grammar] "Must" in reported speech

[tyrp]

Hello!

Could you please clear up the situation with MUST in reported speech? I know it can change into "had to" or be left as it is. When do we change it and when do we not need to do so? Is there any rule about it? Does it depend on whether MUST means an obligation or a supposition?
E.g. It must be John.
Alice said it must be John, (a supposition, so I guess there are no changes necessary).
You must do it immediately.
Alice said I must/had to do it immediately, (an obligation. Are both options possible? Will there be any difference in the sentence meaning?).

Thank you.

 

[tyrp]

Thank you very much, dear Piscean. I don't want to sound obtrusive or ungrateful but could you please explain that insignificant difference brought about by "had to" and "must" in reported speech? I know it must be really insignificant if you say so, but how do you perceive it? If there exist two forms of exression in language, they must serve a certain purpose, right? Thanks a million!