Interpretation of coefficient on interactive effects term in regression analysis
If the following statement is true, Then it means y should increase as either X1 or X2  increases.

I have 2 continuous variables; X1 and X2, both have a positive
correlation on the dependent variable y (continuous)

This is your final model:

$y=aX_1+bX_2-c(X_1*X_2)$


but I wonder why the regression coefficient c of the interaction term
is negative?  what does it mean?

you have a negative sign before the c coefficient which means it tries to decrease y as X1,X2 increases but the data necessitates that it should increase. Hence c is negative.

why if I add only the interaction term (X1*X2) to the model, the
coefficient is positive while if I add it with (X1) and (X2) the
regression coefficient becomes negative? it doesn't make sense!

By adding just X1*X2 to your does it look like the equation below?

$y=c(X_1*X_2)$

Then it makes sense only if c is positive if not then Y will decrease with increase in X1, X2. It makes sense.