Interpretation of VAR model: about impulse function and lag of p

For example, I have three time series, Y,X1,X2. After using time series cross validation and utilizing BIC/AIC to determine the best p as the lag of the VAR model, in which I got p = 1 to estimate the model. I know that to explain the model, we can use impulse function to explain the model, while using variance decomposition to explain the variance of predicted errors.

I have a confusion of p and the explanation of impulse function. Based on the business background, people would expect that the variable X1(t-2) and X2(t-3),for example, can have impacts on the predicted Yt. What I got the p = 1 (lag = 1) seems not working with the ground truth. However, if using the impulse function to interpret, it seems working. Before that, I think I can use the coefficients of the estimated model to explain the Y, such as increasing one unit of X1(t-1) will increase 2 units of Y. However, after checking on the internet and refer related textbook, I realize that I have made mistakes about interpretation.

How I can interpret the model consistent with the ground truth? The predicted effect of the VAR model I have built so far is acceptable.