The "create record" option works when you enter data in the bottom blank row and in certain other specific situations. Creating a new asset record will not automatically create a new employee record nor will the opposite do that either.
You may want to set up a portal to assets on your employee layout or vice versa.
Note that using employee names to link your two tables is not the best approach here. If "Jane Doe" gets married and changes her name to "Jane Smith", changing her name in the employee table will break the connection to any asset records. Using an EmployeeID serial number field in the employee table to link the employee record to a matching number field in the assets table avoids this problem.
I'm unclear as to how a portal would help me. My problem is, if I just use one table, and Sam switches phones with Tina, if I change the name in my "phone" page, it changes ALL of the records, so that Sam has theoretically switched all of his assets with Tina. I would like it so that they are contained in their own tables, and when I alter one, it alters that specific section of the other. Wouldn't a portal just make it act like I only had one table?
A portal allows you to managed the data in one related "child" table from the perspective of a specifc record in the other "Parent" table.
If you have this relationship:
Employees::EmployeeID = Assets::EmployeeID
Then you can place a portal to Assets on the Employees layout. If you find the employee record for Sam, the portal will list all the assets that belong to Sam. If you find the record for Tina, the portal lists all the assets for Tina.
If you enable "Allow creation of records via this relationship" for Assets in this relationship, you can log new assets for Sam by finding his employee record and entering the data in the bottom blank row of the portal.