The DRI refers to elemental zinc, so likely your supplement bottle is saying the pills contain 25 mg of elemental zinc.
For example, approximately 23% of zinc sulfate consists of elemental zinc; thus, 220 mg of zinc sulfate contains 50 mg of elemental zinc. The elemental zinc content appears in the Supplement Facts panel on the supplement container.
Some populations have diminished absorption of Zinc so require higher doses
Vegetarians sometimes require as much as 50% more of the RDA for zinc than non-vegetarians . In addition, they might benefit from using certain food preparation techniques that reduce the binding of zinc by phytates and increase its bioavailability. Techniques to increase zinc bioavailability include soaking beans, grains, and seeds in water for several hours before cooking them and allowing them to sit after soaking until sprouts form . Vegetarians can also increase their zinc intake by consuming more leavened grain products (such as bread) than unleavened products (such as crackers) because leavening partially breaks down the phytate; thus, the body absorbs more zinc from leavened grains than unleavened grains.
The daily upper limit of zinc intake is 34-40 mg in those aged 14 and older so the supplement is below that limit.