If my model says the sky should be blue, and I go out and look and the sky is blue, my model corresponds to reality.

It corresponds to appearance. Models posit causal mechanisms, and the wrong mechanism can predict the right observations.

In general, the correspondence theory of truth means that a proposition is true when reality, or some chunk of reality,  is the way the proposition says it is. Translating that as directly as possible into physical science, a science, a theory would be true if it's posits, the things it claims exist, actually exist. For instance, the phlogiston theory is true if something with the properties of phlogiston  exists. The important thing is that correspondence in that sense, let's say "correspondence of ontological content", is not the same as predictive accuracy. To be sure, a theory would that is not empirically predictive is rejected as being ontological inaccurate as well.....but that does not mean empirical predictiveness is a sufficient criterion of ontological accuracy...we cannot say that a theory tells it like it is, just because it allows us to predict observations.

For one thing, instrumentalists and others who interpret science non realistically, still agree that theories are rendered true other false by evidence,

Another way of making this point is that basically wrong theories can be very accurate. For instance, the Ptolemaic system can be made as accurate as you want for  generating predictions, by adding extra epicycles ... although it is false, in the sense of lacking ontological accuracy, since epicycles don't exist.

Another way, still, is to notice that theories with different ontologies can make equivalent predictions, like wave  particle duality in physics.

The fourth way is based on sceptical hypotheses, such as Brain in a Vat and the Matrix. Sceptical hypotheses can be rejected, for instance by appeals to Occams Razor, but they cannot be refuted empirically, since any piece of empirical evidence is subject to sceptical interpretation. Occams's Razor is not empirical

Science conceives of perception as based in causation, and causation as being comprised of chains of causes and effects, with only the ultimate effect, the sensation evoked in the observer, being directly accessible to the observer. The cause of the sensation, the other end of the causal chain, the thing observed, has to be inferred from the sensation, the ultimate effect -- and it cannot be inferred uniquely, since, in general, more than one cause can produce the same effect. All illusions, from holograms to stage conjuring, work by producing the effect, the percept, in an unexpected way.  A BIV or Matrix observer would assume that the precept of a horse is caused by a horse, but it would actually by a mad scientist pressing buttons.

A BIV or Matrix observer could come up with science that works, that is useful, for many purposes, so long as their virtual reality had some stable rules. They could infer that dropping an (apparent) brick onto their (apparent) foot would cause  pain, and so on. It would be like the player of a computer game being skilled in the game. But the workability of their science is limited to relating apparent causes to apparent effects, not to grounding causes and effects in ultimate reality.