Or does the unit leader have to achieve contact using the movement template?

You cannot place minis via cohesion into base contact with enemy minis.

Page 20:

"When placing a mini in cohesion, it cannot be placed in base contact with enemy minis, unless the unit is in a melee (see "Melee" on page 41)."

What he said. Also, you explicitly have to get the unit leader into base contact to start an engagement.