Dynamic Vibration Absorber

You need to know the vibration frequency and amplitude to design an absorber...

..."Turbine shaft material has its own natural frequency, when turbine rotates on such a speed that frequency of shaft become close to its natural frequency, machine causes noise & high vibrations because of resonance due to matching of frequency."...

http://www.jeacoustics.com/library/FP0729_Evans.pdf

https://energiforskmedia.blob.core.windows.net/media/21242/lateral-turbine-and-generator-vibrations-energiforskrapport-2016-294.pdf

https://en.wikipedia.org/wiki/Dynamic_vibration_absorber

http://www.betamachinery.com/products/vibration-absorbers

http://pioneer.netserv.chula.ac.th/~anopdana/433/ch62.pdf

Re-orient the absorber to the horizontal plane.

How did such a mistake happen?

This brings to mind a saying from when I was in aerospace, "there's never enough time to do it right the first time, but always time to do it over."

Why is the absorber constrained to be vertical? (Assuming you mean operation axis) The operation axis of the spring mass must be coincident with the forces you are attempting to reduce, or it won’t work.

if you work with correct mass units, the deflection will correct to the orientation of the absorber, vertical or horizontal.

To absorb the horizontal vibration of pedestal, the absorber has to be vertical. But will the same formula of deflection as horizontal beam be applicable for vertical absorber.

Yes, you just need to make sure you account for the acceleration of gravity correctly. I still think that the design of your absorber has to have a horizontal freedom to compensate for horizontal vibration, you need a spring and a tuned mass for your absorber, the spring should have a horizontal compression/release, or maybe I don't understand how it really works.