From the description, I feel that the sleeper agent will become my agent once engage a combat.

I try that. Capture an enemy agent, give him Mason Gambit and release. Later in one mission, the sleeper agent appeared. I engaged the combat, but the sleeper agent still fought against me.

Do I misunderstand? How Mason Gambit actually work?

You have to activate your sleeper agent (do you play KGB cause they have just that in their tutorial). Go up to them mutter your words to activate them (it's on your skill bar) and you have an agent that can go anywhere without raising suspicion. See them as a second agent in disguise.

No, you are talking about a control phrase, and OP is talking about Mason Gambit

Woops, must have slipped the line :p

I have figured out myself. the sleeper agent with "Mason Gambit" will turn into your agent next turn after you engage in the combat.

... Which can unfortunately lead to the "Mason Gambit" agent being shot in the face before you can move him. Confused me at first - thought they were shooting at one of my other guys, and was wondering where they came from. That agent ended up surviving the mission though.

I once had two Mason Gambit characters on a mission, and I knocked out the third, so I left that mission with 2 newly-turned agents plus a captive (who ended up becoming a future sleeper agent himself).

Totally loving the MKULTRA stuff so far... ;)