Should I complete the New York job tiers before going to Cuba or mix it up?
You can pretty much tackle it however you want, but remember that for maximum efficiency, you should try to fully complete whatever job tier you are working on before moving to a new one.
The job mastery tiers have always been sequentially ordered, meaning you have to master the lower tiers before you can master the higher tiers. The Cuba ones seem to be separate from the NY ones though, as far as I've seen. I know many players, myself included, abandonded NY for a little while and played around with Cuba even though we still have some tiers to master.
I'm back to working exclusively on NY jobs (finally got Underboss mastered, now working on Boss), but ometimes when I'm getting bored with the grind, I just mix it up a bit. I will also go ahead and do a very high-level job in a tier I haven't started working on yet when I can call for help, so I can get the max experience out of it.
I've posted a list of job mastery items so you can see what you're working towards -- I've stuck with my NY tiers because I really wanted that Private Island (Underboss) and now I want my Golden Throne (Boss)!

I like to complete everything in order but...
Often there are times when you can't because you need certain items, like the cells...
Currently I am trying to complete all of New York before I get fully into Cuba or Russia. However, I have mastered the first tier of Cuba, and level 1 of the first tier in Russia, and am working on the 2nd tier...This isn't to jump ahead to different jobs though. My goal is to have all of the other businesses in other areas running at max effeciency so that I will have a cache of weapons and cash ready for the jobs there, seeing as how it's more difficult to earn money in those areas, at least in the beginning.
Some people like to jump ahead though...the further you jump ahead, the better equipped you'll be. For instance, if your just doing the first level on every tier...you can get to the TNT on cuba quicker...TNT is very powerful. Get yourself 501 of those and you'll be successfull at most attacks far above your level, provided they haven't done the same thing.
Lower tiers tend to have low
Lower tiers tend to have low energy to XP ratios. Do them when you use an energy pack, as this will allow you to do the maximum number of jobs without leveling. For normal leveling, do jobs with high XP ratios, which tend to be on higher tiers or in Cuba.
Tiers
I have to disagree here. As soon as the Boss Tier opens for you, you should work to complete this before any lower Tier as this gives you 2x Energy Regeneration making it easier and faster to complete other Tiers. Also, Cuba is the place to be as the loot there is the best loot around. Do the highest Tier there also as this is where the top loot is which will make you a much stronger player. When you have built yourself up to be a top player you can go back to complete the rest as time allows. The trick is to get 501 each of the best loot for Weapons, Armor, and Vehicles and dump the rest. These best Items are as follows and are in Cuba. "El Padrino" opens after level 130. Top two jobs and bottom job are the best of the best. Defense you need 501 of Guerrilla Squads and this is for both A&D. 2nd job...Supply the FRG w/some Extra Muscle. Top job is for Weapon is Raid the Arms Depot. 1st job in "El Padrino" Teir for the TNT. Need 501 of these and they also work for A&D but some will say the Gaff Hook is better for the Defense. This is not true. MW's will use a Gaff Hook before TNT only because of how the A&D is split but the TNT has the higher total A&D points so is better. That means you have to get rid of all the Gaff hooks in order to use the TNT. Really....this is how it works. The best vehicle to have is the Armored State Car and once again you need the 501 and they are found in the last job of "El Padrino" Tier...Storm the Presidential Palace. Once again this does get complicated and some will argue that these are not the best. But if you do your homework and understand how the Attack and Defense allocations work and how you make which weapons you want to use when Attacking and when being Attacked as there is a differance and young Mafia players don't know or understand this and there are a lot of players who do many games just to push buttons all day and never really use their minds. There is skill and knowledge needed to be the very best Warrior in MW's. Do your research and never believe the first thing you read. Analize all data for yourself. You learn quite a bit from reading walls but there again you have many inexperienced players only going by what happens to them and not the real facts of how the game works. There are many sites that such as this one that are more factual of the game and you can learn much by visiting these sites and comparing all information until you understand the game well. I myself am still learning everyday as there are some very serious players out there who have way more knowledge than I.