If each exchange is independent, how or why does the price move so closely across them? Are people just doing arbitrage?

Like just now there was a big spike in BTC price on both Gemini and Coinbase. Price went a little higher on Gemini it looks like. So is one whale dropping orders on both exchanges or is algorithmic trading across platforms just so fast that arbitrage would never let one deviate much from the others?

Part 2 - why is there an equivalent jump in price of alt coins? I just find it interesting at the exact same moment multiple currencies spike hard and across different exchanges.

It's arbitrage and bots. A couple of them are only actually moving the market though, Bitfinex (biggest), Coinbase, Binance, Huobi.