Your case is documented in the Trillian Security Practices. The mobile device version of the software will store your Google password encrypted on the company servers of the Trillian developers. This allows them to keep your GoogleTalk session alive, even if your mobile device has bad connectivity. It also allows you to use the web version of the Trillian application.
If you reset your Trillian password, then all your stored third-party credentials are lost, since they are encrypted with the lost password. This underlines their claim that third-party passwords are stored encrypted.
Given this setup, it is really the case that the Trillian company server connects to Google with your decrypted clear-text password. Google detects the company server as origin and blocks it if your other devices are far away from the U.S. (see comment by @cremefraiche).
To make GTalk work in Trillian on mobile devices, go to your Google Security Dashboard and mark the server as trustworthy for Google logins.
If you don't like this approach at all, stop using Trillian in the mobile and web version. Delete your Trillian account and change all passwords you ever entered into their application.