So to be clear then, the two chemicals mentioned are not actually combining with each other but rather reacting to the water to turn into hydrofluorosilicic acid and hexafluorosilicic acid?
They do react with each other, but the reaction is ionic opposed to covalent. So they don't really "combine" - they just sort of bump in to each other to form Hydrofluorosilicic acid. But the real key to the reaction is the formation of the hexafluorosilicate anion. I'll elaborate a little.
Because the Silicon atom is large compared to the 4 Fluorine atoms that surround it, H2O and HF are capable of hybridizing with the inner electrons of the Si atom (something that isn't possible in most reactions). The reactions occur like this:
SiF4 + H2O ---> SiF3OH + HF
SiF4 + 2HF ---> SiF6[2-] + 2H[+]
**It looks as though only the 2nd equation is needed to describe the reaction between SiF4 and HF to create the acid. But I think (and I'm really not sure and need someone to back me up on this) H2O more readily reacts with SiF4 to create SiF3OH. This would allow SiF3OH to react at a lower energy to create SiF6[2-]**
The reaction that occurs when you add HF to an aqueous solution is:
HF + H2O <---> H[+] + OH[-] + F[-]
If you combine all of the above reactions you get something like this:
2SiF4 + 2HF + H2O <---> SiF3OH + SiF6[2-] + F[-] + 2H[+]
The above equation can be written in a bunch of different ways, but I think the way I wrote it best shows all of the different "parts" of a Hexafluorosilic acid equilibrium solution. Notice that the SiF6[2-] anion can ionically bond with the 2 hydrogen cations. But since this is an equilibrium solution there are other reactions taking place simultaneously. SiF3OH can take those 2 H[+] cations and create SiF3[-] and H2O; or F[-] can combine with H[+] to get back to HF.
So that was probably more than you wanted to know but I was bored an felt like testing my knowledge of chemistry. On that note I could be completely wrong, can anyone check this?