in my big model I have no detected, that Indexes have been created in an other user than the original tab. This is due to the fact, that in both cards separate selections are possible.
I think, in most cases the index will be under the same user than the table itself.
I would propose, that the user/schmea from the general tab would be transferred to the Index tab. Therefore in the general tab could be a checkbox.
The drop down in the Indextab could be also exist, but swould show at default the selection from general tab and can separately selected, if checkbox is not checked.