I sent my client my link and now they are not connected to me.

Sending an agent your profile link (homesnap.com/firstname-lastname) will only connect a client to you for that single session that they are accessing Homesnap. (this is independent of a Homesnap account and does not require them to make one) 

The user would have to explicitly add the agent as their agent. The idea being, just because I clicked on some link shouldn't mean I want that agent to be my agent. So the user has to take some other action afterward.

In order to brand the client to you and keep them connected, you will need to send them an invite via text or email using the INVITE CLIENTS tool. They will click this link and be prompted to sign up for a Homesnap account or skip.  They will need to make an account in order to brand them to you. If they skip, they will not be branded.