Welcome to the forum, Russ.
VeeCAD uses the standard method to link schematic symbol and board component. The model is not obvious, so please interrogate me as you please.
Your TinyCAD schematic symbol and VeeCAD outline exist separately and never meet up. A TinyCAD symbol is stored in a TinyCAD *.dsn schematic or TinyCAD *.TCLib library. A VeeCAD outline is stored in a VeeCAD *.per project or in a VeeCAD *.per library.
In your TinyCAD symbol set the "Package" attribute to the name of the outline you will be using in VeeCAD. When VeeCAD imports the netlist, it will search the registered outline libraries and grab the first outline that has the matching name and copy it into your project.
So when you make a new TinyCAD symbol, set the package attribute to a name from a VeeCAD library, or give it a new name if the correct outline does not exist in a library.
Practical advice - you definitely need your own TinyCAD library to hold your new symbol. Don't make a VeeCAD library yet, but make any new outlines on the spot, as shown in this video:
https://www.youtube.com/watch?v=G8DCBtyJGsQ . You can transfer new outlines into your own library later on.
Electronic CAD gives you a "factory" for turning ideas into built circuits. It's worth setting up your "factory" if you will use it multiple times.