If rates rise, bond prices decline, so this would tend to decline in price in order to yield a higher interest rate in accordance with any rate hike.
If the rate is 5% on a $1000 long-term bond and the going rate goes to 10%, that $1000 face value bond would have to sell at $ 500 to yield 10%, since it pays 5% of $1000 no matter what the market price of the bond happens to be.
You are right in a way. Since this is a short-term bond fund, the effect would be moderated by the constant maturing and replacement of old bonds with new ones yielding the current rate.
Look at a long term chart of SHV and compare it to LQD which is composed of long-term bonds.