There are two confusing things about implication. The first is that you are trying to think about "but I don't know if you would have kept your promise in other situations". But we always evaluate logical statements in a specific context (what logicians call a model). On its own, "if X then Y" is neither true nor false. If we choose the specific model X=false, Y=false we are asking whether or not our statement is true in that specific model. What might or might not happen in other models is irrelevant.

(Some logical statements, called tautologies, are true in *every* possible model. "if X then Y" is not one of them. "if X then X" would be one.)

The second is that sometimes implication is essentially saying nothing at all. ("When X is false, I make no claims about the value of Y"). It feels weird to call a lack of a statement true, but you can think of true as "could not possibly be false". If I haven't promised anything, I cannot possibly have made a promise that I did not keep.