Here we go... the answer to the "tassel question"!

...during commencement ceremonies, ... candidates for degrees wear the tassels on the right front side before degrees are conferred and shift them to the left at the moment when degrees are awarded to them.

Plus a list of fields of studies along with their respective colors:

Arts, Letters, Humanities — White
Business — Drab
Economics — Copper
Education — Light Blue
Engineering — Orange
Fine Arts — Brown
Journalism — Crimson
Kinesiology — Sage Green
Law — Purple
Library Science — Lemon Yellow
Medicine — Kelly Green
Music — Pink
Nursing — Apricot
Philosophy — Dark Blue
Public Administration — Peacock Blue
Public Health — Salmon Pink
Science — Golden Yellow
Social Science — Cream
Speech — Silver Gray
Theology and Divinity — Scarlet

Source: University of Idaho Faculty Handbook and Sonoma State University Commencement Symbols