I've found that they start to move based on temperature and flow but it also depends on the species. Rainbows and cutts move first because they are spring spawners so they will stage at the mouths of creeks and streams before going up to spawn. Generally they are looking for water temps around 6 to 8 degrees. Browns, bulls, whites move later and generally its when the flows and water levels start consistently rising. I use this online tool to track flows and water levels.
https://rivers.alberta.ca/