Q:

Does "remembered to" mean that the action was done? 

John remembered to call Alex. 

Does this sentence imply that John called Alex?  Or does it merely mean that John remembered that he needs to make a call?  That is, is the sentence 

John remembered to call Alex but John did not call Alex. 

contradictory? 

A:

The ordinary meaning of John remembered to call Alex is that John did call Alex, but you can also write lots of sentences like John remembered to call Alex but forgot again immediately. 
The ordinary way of separating the remembering and the doing would be constructions such as "John remembered he wanted to call Alex, but was distracted and then it was too late."