Why amazed? Not only is this incredibly easy to pull off in China, it's the norm. Things happen fast. You look over apartments for a couple of days in a new city, negotiate and sign lease, move in soon after. Most apartments are owned by private landlords, so you either find them directly or work through a local agent (bunch of sharks, those). Of course, it helps to be familiar with China, and have enough inherent knowledge to know instinctively what a good apartment is, and what a good deal is. It gets easier with practice.

Move in, register with wuye (apartment management), register with neighborhood police, get utilities set up or transferred (usually not much issue since they are often in landlord's name). Most utilities in China are done with prepaid account cards that are topped up, rather than billed in arrears such as done in USA. Have moving company send down stuff from previous city.

If it's a longer term move rather than a temporary placement, employer needs to get the local Labor Bureau to redo the Work Permit, local Tax Bureau to get the required remittances going, and local Public Security Bureau to re-issue the Chinese Residence Permit for Foreigners for that new jurisdiction. This paperwork stuff is the real pain in the butt, not the physical logistics part.

If you have a really good deal in your old city and will go back there a lot, maybe it makes sense to keep the apartment, but usually rents in places like Beijing and Shanghai are way too expensive to do this. Tossing away USD 1000-2000 per month just for a bit of convenience is extravagant unless you're on the Executive Plan. And if you already have friends in the old city, you'd just stay with them for short visits. Or stay at a small hotel/serviced apartment you've managed to strike up a good relationship with the management...assuming you're paying for things yourself and employer isn't picking up tab.