I instinctively agree with you completely, Dmitry. I have never heard "with" used in this way, although I have heard it in an instrumental sense e.g. he talks with a German accent or she talks with passion about the European Union.
In both these cases, though, I think it would be preferable to use speak.
However, on the Internet, I found this grammar lesson . So it seems that this is a situation where American usage has evolved in a manner contrary to the British one.
Note: "To have a talk with someone" is a common British usage. But having a talk with is not synonymous with talking to. There is a slightly ominous tone to it. A child should expect a lecture, an adult a confrontation, at least.
"He didn't deliver the goods on time? Well, I'll have to have a talk with him about that..."
This appears the converse of the American usage. In Britain, it is a talk with someone that implies an aggressive monologue.
"have a talk with" CAN mean the same thing in the US with context like the example you gave. Almost any formula using "talk" can be understatement/euphemism for 'scolding' with the right tone, context. Probably "give a talking to" is pretty reserved for this use in the US (I'll have to give him a good talking to") Something different, a one-sided conversation is: "talk at someone" (she'll talk at you for hours if you let her)