I’m not absolutely sure:
Did you ever get another result? (If so: Please tell me a version that did it.)
What do you mean by “… since a new formatting applies …”. (New in what sense?)
I would expect to always get the “Illustration Index Items” shown as a whole with the character properties connected to the paragraph style applied (‘Illustration Index 1’ by default). The index generator won’t worry about the styles used for parts of the original caption.
Editing after another comment:
So is there any option I could leave the caption content in its source formatting (something like “Keep source formatting”)?
As there isn’t an option as you already looked for I cannot see a way to do so. The only thing you can actually do is to adjust the character formats after building the index manually in every place where wanted/needed, To be allowed to do so you have to “uncheck” the option ‘Protect against manual changes’.