Hi,
Yes this is correct.
YC has one master catalog which has everything in it (think of it as hierarchy of all products in the "known universe"). Each shop can "use" some (or all) of master catalog branches. This means that if you have multiple shops that have access to same categories, then both have equal rights to access/modify those categories. This is if we are talking about straightforward category assignments.
Now if you do not want to share categories - then you can create two different branches in master catalog and then assign only those branches that each "shop" should see. Then you can import/add products in relevant branches. Note that product to categories cardinality is many-to-many, so you can share products as well or keep them restricted by assigning them to relevant branches only. This means there is plenty of flexibility to setup the branches that you need for specific shop.
Regarding shop admin "access" - whatever categories are assigned to shop that is what is available to shop admin.
NOTE: there are 2 roles: Admin, and Shop Admin. Make sure that your user has only Shop admin role (the other one is system admin with full access to everything).
If everything setup correctly your Shop admin user will only see part of catalog assigned to their shop on ALL views.
Regards,
YC team
P.S. if you have a question you should not put "issue" in the title as this suggests a problem and this is not the case