Ah, a picture is worth a thousand words.
Seriously this time, the chief culprit are the pants. You need a much higher rise, and they could be a little looser around the leg and hips and possibly the waist. Shirt is too snug through your shoulders, you're not a skinny guy, and a more traditional cut like Brooks' Madison cut would suit you far better.
What's happening is any time you move your arms and upper torso, there's no slack, so your shirt will pull out more than it otherwise would, and because there's a lot of space to your belt line the shirt begins to become untucked.
All shirts will blouse a bit more as you move around, the fit issues I've mentioned just make it far more significant. If you insist on wearing your pants that low, you could look for a shirt cut as a long, which should have a longer shirt body. Might help with the untucking, but won't do anything for the blousing as I've explained.