Sometimes, you're not forced to serve a sentence consecutively, meaning Weiland could do it on off time from the tour. Also, when forcing you to jail could cause large financial harm to many others, they allow you to work while heading back to jail to serve time when you can. Robert Downey Jr. was once able to leave jail each day to film a movie.
The fact that he was sentenced to hours, not days, tells me he will be allowed to serve the time and work around his touring schedule.
Of course, I could be wrong. Have been before.