[Guido]

Just like I commented on the first season's episode that introduced Tama to the audience: "There's no freaking way that tigers exist in Africa".

So, what Nagi did to pet Tama?

Spoiler:

She kept him as a cat, because she took Isumi's word for granted that Tama's a cat, and yet she lovingly raised Tama for both lost their mothers and ensured to protect him from harm everyday.

It worked out as Tama got directions through a GPS-locator, cell phone from anonymous user 110, which was revealed to be Nagi at the end of the episode. However, let us take notice that Tama's secret remains safe, since Nagi never got the slightest idea that user 112 was actually Tama.