Peter Parker was no stranger to the strange and fantastical, you spend long enough in New York and it was inevitable that you would stumble across some kind of mystical or scientific miracle that blew wide open just how vast the unknown truly was. Of course, as Spider-Man he was shown such things regularly, and every time he was witness to something new and awe inspiring he was reminded of how little he knew in the grand scheme of things.
Which is why him waking up in a prison one day fully suited up and in the midst of a prison riot doesn't even phase him, he's not all that surprised so much as he is just really, really frustrated.
Figuring out where this "Gotham" City was located could wait til later, right now he had a prison full of inmates to take care of.
After the events of Miles Morales and Spider-Geddon, Peter winds up in the Arkhamverse at the start of Asylum. He's confused, annoyed, and also really cold on account of it raining. Batman's got a 5 minute head start on Pete, but considering it's Batman he's probably subdued a ton of inmates by now.