Just to be clear, a Church member's Church Account and their Family Search account are separate accounts and are not linked directly. In fact, a member or nonmember can have multiple Church Accounts and multiple Family Search accounts. Changes in the profiles of any of those accounts will not affect any of the other accounts. The key that connects one Church Account to one Family Search account is the membership record number (MRN). It is the ability to have multiple Church Accounts and multiple Family Search accounts that causes confusion and difficulties for some Church members.
You are correct that if the menu item "Temple" is displayed on the Family Search menu bar then that Family Search account has a MRN registered in that user's profile. Only work done with that Family Search account will include temple information for that account holder.
Even the display of the "Temple" menu item is not a good indicator the account has been properly set up for that account holder. Always check the account profile for the correct MRN. Sometimes, and because of long ago traditions, member couples will use their spouses MRN when creating accounts.