Its usually not a problem. Only a small amount of air will inflate the tube enough to keep the valve from being pushed inside the rim.
For good puncture protection get better tires. Can't tell you what to get since you're on a hybrid. Mine are 700x23 Continental GP4000. I average about 1500+ miles between flats and I use whatever tubes are on sale.
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The Lord is merciful and gracious, slow to anger and abounding in steadfast love. - Psalm 103:8
I am a cyclist. I am not the fastest or the fittest. But I will get to where I'm going with a smile on my face.