Why are "transfer payments" not part of GDP? It is well-known that transfer payments are not counted in GDP (e.g. wikipedia 1 and wikipedia 2).

For instance, exercise 2.c in Chapter 2 of Jones book's Macroeconomics ask to calculate how much GDP changes if:


  During a recession, the government raises unemployment benefits by $100 million. 


The official solution says:


  No impact. This is a government transfer payment, not a government purchase of a good or service.


But, what if that transfer is spend in goods? Would that not increase C? What if just a portion of the transfer is used to buy goods?

In fact, an article from Business Insider states the following:


  While transfer payments are not included in GDP, they are largely put in the hands of those who spend most of the money immediately. Therefore, transfer payments show up in GDP as increased personal consumption.


I am puzzled. Why transfer payments do not increase GDP? I would have thought that it depends on whether that money is spent. Also, is this completely independent on where that money comes from? What if it comes from borrowing abroad, or nationally, or from taxes?
Transfer payments aren't included in GDP to prevent double-counting. 

The reason the author's question is troubling you is because the answer externalizes everything that happens after the payment has been made (which is when the money from that payment DOES get factored into GDP, see below). I assume it does this to reinforce that transfer payments aren't counted in GDP, but you are right to question what's going on here. 

That \$100 million is transferred from the government to consumers, who will presumably spend a good portion (say, \$98 million) of those funds on goods and services, at which point those funds would be added to GDP. If we had included the transfer funds in GDP, the change reflected would be \$198 million instead of the more accurate \$98 million.

You can also have an example on a much smaller scale: 


You give your child \$5 to buy a burger; none of that is added to GDP. 
Your child spends \$4.75 on the burger; \$4.75 is added to GDP.