Yes, it does take 2 turns.
When you board an allied TRN, once on board you are “cargo” of the TRN. That means that, upon boarding, you are part of the TRN, and your further movement passes to the TRN. Then, on your nation’s NEXT turn, you can offload.
OM Page 31 :
Being carried on a transport counts as the land units entire move; it cannot move before loading or after offloading.
Boarding is movement. Offloading is movement. Therefore, you cannot board, and them make another mvoement to offload in the same turn.
The real kicker for clarification is in LHTR.
LHTR uses the same wording in the description of transports… with one MAJOR clarification…
Land units belonging to friendly powers must load in their controllers turn, be carried on your turn, and offload on a later turn of their controller.