Assuming that you are talking about NCAA rules, then yes, the shot clock should've been reset to 30 or 35, depending on whether it was a Men's or Women's game.
If you're talking about a HS game, then nobody here knows what should've happened b/c there are no NFHS rules governing the shot clock. You'll need to check with a state association to determine what the shot clock rules are for your state.
If you're talking about an NBA game, then the officials were correct and the shot clock should remain at 19. In the NBA, if a defensive foul is committed in the frontcourt, there is no reset if there are more than 14 seconds remaining on the shot clock. If there are less than 14 seconds remaining on the shot clock, then the shot clock is set to 14.
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Any NCAA rules and interpretations in this post are relevant for men's games only!
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