Is it always necessary to have a c-section with twins?

No. Plans can change. Mode of delivery (vaginal, abdominal) depends on many things up to time of delivery: presentation and sizes of the babies, condition of the babies, condition of the mom, placenta locations and presence of bleeding, heart rates of both babies, pregnancy complications, etc. This decision is best made at the time with mom and the most experienced OB provider present or available.
Advisable. Necessary not always, advisable always! 80% of all twins deliver via cesarean section in the us nowadays, for fear of increased perinatal death or injury to the second twin. I recommend cesarean section for all twins at this time, especially if bilateral tubal ligation is planned - talk to your maternal-fetal medicine specialist to see if this a good option for you.