Judging by the word topolect, I think you are most interested in this:
Phonetic realization of Mandarin tones in principal dialects
(scroll down to the table with the caption 'Phonetic realization…'). This is how people from different regions will most likely realize the tones when they are speaking mandarin with the "local flavour", whereas educated people, tv/radio hosts will perhaps strictly stick with the Standard Mandarin, even if they are not from Beijing.
Dialects have their own tone systems, with a varying number of tones. Unfortunately, phonological material is only available for a very few dialects, e.g. Hokkien, Cantonese, Shanghaiese [if you consider these to be dialects, I think they are languages on their own]. I used to do research on the tone systems of tonal languages, and there are at least two types of notations, the one with numbers describe the pitch, just as the OP demonstrates, and there is another kind of notation which uses "sticks", like ˥ Mandarin 1st tone, etc. (unfortunately this site doesn't support pasting them, please refer to the table in this article.
The Chinese people, when they are to discuss the tones for any reason, including linguists, will use tone names, that have existed since centuries if not millennia, e.g. 阳平、去声、上声, etc. These are less accurate, since they are not absolute notations of a tone contour and could vary across dialects and regions. A good reference would be this table.