Transport for Santiago de Compostela to Tui

Take the train at 17:30h from Santiago to Pontevedra (IR9173), change to Vigo (Reg 12589) and finally change for Valenca (IC422, 19:56 Vigo-Guixar). Spanish arrival time will be 20:32h. Don't change the watch and go back the few steps to Tui, which is <30min walk.

If you know how to make the bus change in Vigo, you can directly go to Vigo with monbus and take atsabus somewhere in the city. The 5pm bus has 3 stops in Vigo:
18:25 Rúa Areal (Vigo) - (Vigo)
18:27 Travesía de Vigo, 41 (Vigo) - (Vigo)
18:30 Vigo (Estación de Autobuses) - (Vigo)
The internet price For Santiago-Vigo is even lower than the standard 6,80€, but I guess that doesn't matter.
The last Atsa bus leaves Vigo 20:30h. http://www.atsahorarios.com/entreguavigo.php

You might also be able to change buses at the Vigo bus station.

The Santiago airport bus makes a stop at the Santiago bus terminal, where you can get a bus to Vigo.

Try Rome2rio.com

There is also a direct ALSA bus from Santiago bus terminal to Tui and Valenca
17:30 Departure, Santiago Compostela
18:15 Stop-off Pontevedra, Spain
19:00 Stop-off, Vigo , Spain
19:30 Stop-off, Tuy , Spain
18:35 Arrival, Valença Portugal

From SCQ airport you have a short ride with Freire; http://www.empresafreire.com/html/ingles/seccion3z.php
15:50 and 16:20 will be good for you (3€). A Taxi should cost ~20€.

It doesn't look like you can buy a ticket to Tuy with Alsa. Santiago-Valença is possible, but 30€.
Vigo-Valença costs 12€ (again no Tuy ticket price).
Monbus only charges 6,80€ for Santiago-Vigo, the international ALSA bus charges about the double.