Alterations help!!

Take the dress back and have them fix it. I had cups sewn into my dress as well and the fit was perfect

It seems like you have low density breasts that lack volume - which by the way is totally normal. With such a structured dress, its pretty normal that your breasts would shift and fill out the cups less with your arms raised. That's just how physics works! Its also why I hate strapless dresses for anything other than a quick photo or two (my boobs would also "move away" from the cups in a dress like this, and I like to throw my arms up in the air when I dance).

What does the back of your dress look like? If the dress is taken in at the bust, it will eliminate the gapping somewhat. Your boobs will be more squeezed and lifted with your arms down, but when you raise your arms they'll sit in the cups without gapping so much. If the back of the dress is high (the level of a strapless bra to maybe an inch or two lower), you should be able to have the overall bust circumference measurement taken in no problem, as they can just take in the dress from the side seams. If the back of the dress is low and the front is mostly boning and heavily structured material, it might not be possible to get that pulled in look because there is no fabric to make tighter to physically pull in the dress. The dress needs to be taken in regardless, but whether or not there is fabric at the back ribcage will impact how much support doing so will give your breasts.

It doesn't look like the people who did your alterations were very experienced. They should have done your initial measurements/fitting with whatever undergarments you were planning to wear, and the dress should have been marked/pinned at the appropriate point where the seam should be to provide support, not just cover the measurement. That might mean that the dress is actually an inch tighter than your relaxed bust measurement, to get the lift and support you want. Additionally there shouldn't be any rips or unsewn pieces during your final fitting.