Do not expect the motorcycles to let you pass when crossing the road. Instead, they will just drive around you. Cars and buses will stop, but you have to make sure you catch their attention. A lot of the traffic lights are not functional so you have to take the initiative to cross the street and hope that traffic will stop for you.
Also, catching a cab from the airport to Phuket is also crazy scary and I would highly advise you to book your airport transfer in advance. Not only is it cheaper, but it is much safer than trying to catch a cab from the airport. I’m not kidding you when I say that taking the taxi in advance from the airport to Phuket was one of the scariest moments during my year of travel. Scary AND scammy! We did our research and made sure to be aware of the taxi scams but we still ended up in a taxi with one of the sketchiest drivers ever! Read this thread about taxi scams if you want to learn more.