There are currently two choices for how TaleSpire will react when it sees community made content you don't have installed.

By default it will pop up a dialog where you can choose either to download them all, or to view the missing creatures in the library.

If you choose the library you will be shown the missing content and you can decide whether to install some or all of them.

If instead you choose to trust all community content, then TaleSpire will install anything you need from the official repository automatically.

Regardless of the setting, if the creature is not on the official repository (on mod.io) TaleSpire will not be able to find it.
So if your friend has a .tsMod file that you do not, they will have to send it to you so you can install it.

We have a guide for how to do that over here -> Guide: Adding creatures from .tsMod files