Associate Product to Vendor

- I have an Asset which originally have the following information.
      Product Name = "blank"
      Vendor Name = Mang Jack's Surplus

- During audit, the Product Name (which was originally empty) and the Vendor from whom the Asset was purchased from are updated to:
      Product Name = Dell R710
      Vendor = Dell Authorized Distributor

- When I go to Admin>>Vendor and click on the Dell Authorized Distributor, Products Tab - Dell R710 is not listed as an associated product.

Is this the expected behavior i.e. No automatic linking of the Vendor with Product Name?

What if in the second step, I only update the Product Name. Will Dell R710 be an associated product for the Vendor Mang Jack?

Thanks in advance!