Generally correct. The Transition Altitude is defined by the country aviation authorities, which mostly correspond the FIR boundaries. Especially in Europe it’s possible that an airport is controlled by a different countries FIR by local procedures and country agreements.
ATC wise, upon entering Cuban airspace the controller will instruct for Flightlevel (FL) 60, which basically means flying at 6000ft with standard altimeter setting. Mind that Cuba uses hPa as pressure unit, so your standard is 1013 hPa.
There’s also a Transition Level (TL) assigned by ATC depending on local pressure, ensuring minimum of 1000ft vertical separation between 3000ft on local altimeter and the lowest usable level, i.e. FL40 or FL50. However ATC will tell you and your cruise altitude FL60 is safe anyway. The Jeppesen chart says: “Trans level: By ATC” accordingly.
Hope this helps…