How is this bathtub overflow drain supposed to be assembled?

Yep. The tabs should be on the inside to keep it stabilized and centered and there should probably be a ring of plumbers putty between the tub wall and the overflow pipe if the black part isn’t some sort of adhesive sealant. Otherwise just center the pipe and make sure the black ring is sealed tightly against the tub. It may help to heat the tub wall with a hair drier to get the best seal.

Note: Do not use the hair drier in in the tub while water is in the tub.