Supercapacitor Voltage Draw
When I attach the capacitor to my digital power supply, it starts charging, and the voltage slowly increase to be more than 2.5 volts, at which point I turn it off.


You should not connect a (super) capacitor to any voltage higher than its rated voltage.

A minor over voltage may only reduce lifetime, but a higher voltage can cause gas generation and/or breakdown of dielectric material. That can result in explosion and/or chemistry leakage.


  I was wondering will it draw more than 2.5 volts from my buck converter? If so how do I stop it?


It will "try" to charge up to whatever voltage you apply. But as I pointed out, at some point it will cause catastrophic failure.