I'm not the best person to talk about this since I mainly play low-limit SNGs, but I'll throw out some ideas for you. (Also I'm just a terrible player!) Hopefully others will chime in.
In a MTT, considering whether to call an all-in depends on a number of things, like your stack size, opponents stack size, current blinds, # of players left/proximity to bubble, if there are re-buys etc etc. It also depends on your
bankroll, the stakes you are playing at, and what you are comfortable with.
Some people would risk their tournament life early on for a huge chip lead. There are some cool videos about this... check out this one, its sort of an overhead theory vid about risk/reward strategies in a MTT:
https://www.youtube.com/watch?v=0b_2yYkviDQ
If you aren't already, familiarize yourself with basic odds and
pot odds. There is a cool article on here called "Odds for Dummies," that explains these concepts quite well.
In a tournament setting, players will often take routes that secure them a decent amount of chips, while avoiding small risks, even if it means they could earn more.
This seems to be the scenario your opponents are putting you in. If your opponent puts you on a draw, and he has a made hand, he can either chose to make you pay to draw, or he can blow you out of the pot. These all-ins may be the ladder, and there is some credit to this strategy depending on the size of the pot in relating to stack sizes, and other things.
So... when to call? I'm going to guess and say its more often correct to fold, especially when our Opponent shoves on the Turn. The urge to call is probably more often frustration... I started a thread recently about these flop all-ins in a SNG... I get so mad when my opponent refuses to play poker lol, but it is part of the game and we need to learn to counter this strategy.
The more accurate you can get with hand reading the better when considering a call. Often times if he shoves on the flop, you will have only a vague idea of what Villain has. But did he open raise pre flop? Limp-call? Call your raise in position? 3-bet? These combined with your previous reads on Villain will give you a sense of where you stand.
Then its just a matter of knowing your outs. Most people understand the basic outs for flushes and straights, but maybe your overcard will give you 3 extra outs. Maybe you also have a gut-shot strait draw... having a precise knowledge of where you stand is vital to calling an all-in.
Next is pot odds... am I getting a good price to call? Since I'm not too familiar with tournament play, you may want to look into how the ICM (independent chip model) affects tournament play at different stages. This could slightly warp your actual money EV, so make sure you are getting significantly better odds to call than you normally would. I can't explain this too well, but be sure to look up this concept and read how it applies to MTTs.
And, of course, the last circumstance is being pot committed. Sometimes you'll be forced all-in yourself due to your stack size and odds. It all really depends on those things (Stack size + pot odds). Consider where folding leaves you. If you fold, will you be crippled for the rest of the tournament? Will you be dead by the time the blinds come around? etc, etc..
If this is a play Villain makes against you a lot, consider beating him to the punch... in
some cases it may be better to shove on the flop than to check.
This is mainly just a point to help you understand your opponents strategy, but when you bet, you can win in 2 ways (opponent folds or you have the best hand). When you call you can only win by having the best hand. Shoving yourself gives what is known as fold equity.
I'd ask more questions here and post hand histories so we can get a better idea of the situations you have been put in.