Regardless of the time of day you decide to fly, the ticket price will remain around the same. Book flights from Tucson to Phuket as you normally would.
In terms of precipitation, rainfall in Phuket ranges from 1.2 - 16.1 inches per month. September is typically the wettest month, when rainfall can reach 16.1 in. January is typically the driest time to visit Phuket when rainfall is around 1.2 in.
If weather is an important factor for your trip to Phuket, use this chart to help with planning. For those seeking warmer temperatures, March is the ideal time of year to visit, when temperatures reach an average of 82.4 F. Travelers looking to avoid the cold should look outside of January, when temperatures are typically at their lowest (around 80.6 F).