This is on SmitchCart 4.67 where there are several shipping types available during checkout.
"Calculate Shipping" will do as it says and update the ship method dropdown with rate info, and also updates the displayed value for shipping & handling in the cart.
The problerm is that "Calc Shipping" doesn't use the selected ship method when initially running the calculation and setting the displayed value of S&H - it calculates S&H using the first ship method in the ship method dropdown, regardless of whether it's selected or not.
Once that happens, the customer sees the mismatch, and the only way to have an accurate S&H is to choose a different ship method to update the display, then choose the origianlly selected ship method to reflect the correct S&H for chosen ship method.
Short answer? Please have the Calc Shipping event calculate to the ship method that is selected in the dropdown.
This is what customers commonly do - select the ship method first, then click the Calc Shipping to get the rate.