Hope you're enjoying your weekend.
Contractions can be very confusing alright if you're not sure what they stand for.
First of all, both "It's two years since we last saw each other." and "It's been two years since we last saw each other." are both correct. So no, don't worry :) Your teacher certainly hasn't given you wrong information.
In the FIRST sentence, "It's two years..." the contraction stands for It + is
In the SECOND sentence, "It's been two years..." the contraction stands for It + has
The second sentence is using the present perfect "It has been two years..." and would be more typical in British English.
The present perfect is used for an action that began in the past and continues up until now.
The action is this case is the two people not seeing each other.
The first sentence is using the simple present "It is two years..." and is more typical in American English. American English uses perfect tense a lot less than British.
It's certainly not WRONG! But British people might think is sounds a little strange.
Hope this helps!