Hello, non-US fellow here. Can someone point out to me, why this is not the case - I assume that is the reason this got slightly downvoted - or do people just have different opinions about the meaning of "control"?
The JCS have a very important role but their control is mostly administrative (doctrine, assignments, equipment, promotions, etc.).
This is the case in funding the US Department of Defense. The overall budget is set by the Congress (and subdivided innumerable times afterwards by the DoD agencies and departments), so saying that civilians control the military in the US is both true in the operational sense (the military is part of the Executive Branch, and thus under the President, a civilian), but also in a financial sense.
More info about the US budget process (which bears a strong resemblance to making sausage..) can be found here:
The "Commander in Chief" (President) has somewhat wide berth of power over the military and can somewhat do what they want with the military. Congress has some checks for what the Commander in Chief can do, but traditionally the CiC has been able to basically send troops to wherever whenever.
In terms of actual citizen power over the military, no. Everyday citizens have no power or direct say in the military.