Shutter and shakes

There has to be more to the story that you may not know about. You are describing a misfire, and that cannot be caused by simply disconnecting the battery. Also, it does not matter if the negative or the positive battery cable was disconnected. Both are required for the electrical system to work, so removing either one of them does the same thing. It is standard procedure for safety to remove the negative cable first when removing both, and to reconnect it last. That is because if you try to remove the positive cable first and the wrench slips and contacts a metal part of the body, or metal brackets, a huge spark will occur. It is possible for that short to turn the wrench red-hot and melt it. Instead, once the negative cable is removed first, if the wrench touches the body and the positive cable at the same time, nothing will happen.

As for the crank/no-start condition once the battery was reconnected, that is extremely common and does not mean anything was done wrong by the salesman. All of the data in the engine computer's memory was lost when the battery was disconnected. Fuel trim numbers and sensor data will start to be rebuilt as soon as you start driving again, except for "minimum throttle". Until that is relearned, the computer will not know when it has to be in control of idle speed. The engine may not start unless the accelerator pedal is held down 1/4". You will not get the nice idle "flare-up" to 1500 rpm at start-up, and it will tend to stall at stop signs. There are very specific conditions that must be met for the computer to relearn minimum throttle. To meet those conditions, you have to drive at highway speed with the engine warmed up, then coast for at least seven seconds without touching the pedals.

What problem or symptom originally brought you to the repair shop, and why was it necessary to disconnect the battery? Testing the battery does not require removing a cable, and testing the charging system also does not require taking a cable off unless the tester was real old, as in from the 1970's. If there was a diagnostic fault code in the engine computer, that got erased when the battery was disconnected, so that valuable information was lost. Your computer is capable of detecting well over 2,000 defects, and it will set a fault code specific to each of them. About half of those codes refer to something that could adversely affect emissions. Those codes turn on the check engine light. If the fuel mileage is as bad as you described, emissions has gone way up and there should be a diagnostic fault code to indicate the circuit or system that needs further diagnosis, or an unacceptable operating condition. The people at many auto parts stores will read those codes for you for free. Start with that. If there are any fault codes, be sure to write down the code numbers, and post them here in your reply.